JP2010540936A - Reactor dosimetry application using parallel 3D radiation transport code - Google Patents
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Abstract
本発明は、広義には、新規のパラレル３次元放射線輸送コードとマルチプロセッサ・アーキテクチュアを利用する放射線場分布計算方法に係わる。コードはドメイン分解アプローチを利用してアルゴリズムを解く。例えば、角度ドメインおよび空間ドメインをサブセットに区分し、これらのサブセットをそれぞれ個別に割り振り、処理させることができる。 The present invention broadly relates to a radiation field distribution calculation method that utilizes a novel parallel three-dimensional radiation transport code and a multiprocessor architecture. The code uses a domain decomposition approach to solve the algorithm. For example, angular and spatial domains can be partitioned into subsets, each of which can be individually allocated and processed.
Description
この仮特許出願は２００７年９月２７日に提出された米国仮特許出願第６０／９７５，５２５号に基づく優先権を主張する。 This provisional patent application claims priority based on US Provisional Patent Application No. 60 / 975,525, filed Sep. 27, 2007.
本発明は広義には放射線場分布の計算に係わり、特に原子炉のキャビティおよび内部コンポーネントの中性子線量応答の予測に有用である。 The present invention relates broadly to the calculation of radiation field distributions and is particularly useful for predicting the neutron dose response of reactor cavities and internal components.
中性子およびγ線輸送アプリケーションの線形化ボルツマン方程式（ＬＢＥ）の数値解を得るには種々の方法を使用することができる。離散座標法（ＳＮ）は特に核工学分野において採用されるこの種の方法の１つである。ＳＮ方程式の数値解法は位相空間、即ち、角度ドメイン、空間ドメインおよびエネルギー・ドメインの同時離散化によって達成される。位相空間を同時離散化する結果として、ＳＮ方程式中の多数の未知要素に遭遇するから、この問題を解くには厖大な計算資源が必要になる。 Various methods can be used to obtain a numerical solution of the linearized Boltzmann equation (LBE) for neutron and gamma ray transport applications. The discrete coordinate method (S N ) is one such method employed in the field of nuclear engineering. The numerical solution of the SN equation is achieved by simultaneous discretization of the phase space, i.e. angular domain, spatial domain and energy domain. As a result of the simultaneous discretization of the phase space, a large number of unknown elements in the SN equation are encountered, and a tremendous computational resource is required to solve this problem.
大規模な３次元中性子およびγ線輸送アプリケーションでは、ＳＮ方程式を利用してＬＢＥの数値解を発生させるのに必要な主記憶装置は典型的なシングル・プロセッサ・ワークステーションの現時点での計算能力を超える可能性がある。例えば、約１５０万個の空間格子、Ｓ８求積セット、散乱核のＰ３展開、および４７の中性子エネルギー群を特徴とする典型的な２ループ加圧水型原子炉（ＰＷＲ）に関する完全な３次元中性子輸送の問題を解くには、約４５ギガバイトの主記憶装置が必要になる。このような問題を解くのに必要な有意な計算資源に、シングル・プロセッサ・ワークステーションは含まれない。 For large 3D neutron and γ-ray transport applications, the main memory required to generate a numerical solution for LBE using the SN equation is the current computational power of a typical single processor workstation. There is a possibility of exceeding. For example, full three-dimensional for a typical two-loop pressurized water reactor (PWR) featuring about 1.5 million spatial lattices, S 8 quadrature set, P 3 expansion of scattering nuclei, and 47 neutron energy groups Solving the neutron transport problem requires about 45 gigabytes of main memory. Significant computational resources needed to solve such problems do not include single processor workstations.
マルチプロセッサ計算アーキテクチュア、即ち分散メモリ・アーキテクチュアを活用するための新しい解法アルゴリズムを開発することによってこれらの困難を克服することが望まれる。例えば、多数の物理的に独立したワークステーションを、ネットワーク・バックボーンを介してリンクして、いわゆるクラスタ・コンピューティング環境を確立することが望ましい。近年、特に学術的な計算や大規模な数値シミュレーションの分野においてこの種の計算プラットホームが広く採用されている。但し、クラスタ環境の能力を活用するには特殊なアルゴリズムを考案する必要がある。 It would be desirable to overcome these difficulties by developing new solution algorithms to take advantage of multiprocessor computing architectures, i.e., distributed memory architectures. For example, it is desirable to link a number of physically independent workstations over a network backbone to establish a so-called cluster computing environment. In recent years, this type of computing platform has been widely adopted, particularly in the field of academic calculations and large-scale numerical simulations. However, it is necessary to devise a special algorithm in order to utilize the capacity of the cluster environment.
従って、マルチプロセッサ計算アーキテクチュアを活用するためには、ＳＮ方程式に関する一組の解法アルゴリズムに改良を加える余地がある。また、中性子およびγ線界分布のような放射線場を計算するため、ＬＢＥの数値解を求める方法にも改良の余地がある。さらに、原子炉用として、正確且つ効率的に線量応答を予測する方法にも改良の余地がある。 Therefore, in order to utilize the multiprocessor computing architecture, there is room for improvement in a set of solution algorithms for the SN equation. In addition, there is room for improvement in the method for obtaining a numerical solution of LBE in order to calculate a radiation field such as neutron and γ-ray field distribution. In addition, there is room for improvement in methods for accurately and efficiently predicting dose response for nuclear reactors.
角度ドメインおよび空間ドメインから成るドメイン群から選択されるドメインを含むドメイン分解アルゴリズムより成る３次元放射線輸送コンピュータ・コードを利用し、前記ドメインをマルチプロセッサ・コンピュータ・アーキテクチュアに割り振り、それぞれ独立に処理させる放射線場分布の計算方法。 Radiation using a three-dimensional radiation transport computer code comprising a domain decomposition algorithm including a domain selected from a domain group consisting of an angular domain and a spatial domain, wherein the domains are allocated to a multiprocessor computer architecture and processed independently. Field distribution calculation method.
放射線場分布を計算するためのコンピュータ・プログラム。このプログラムはコード・セグメントを含むが、該コード・セグメントは実行されると、角度および空間ドメインをサブセットに分割し、これらのサブセットをそれぞれマルチプロセッサ・アーキテクチュアに割り振り、それぞれ独立に処理させる。 A computer program for calculating the radiation field distribution. The program includes code segments that, when executed, divide the angular and spatial domains into subsets, each of which is assigned to a multiprocessor architecture and processed independently.
本発明は１つのシステムに関して放射線場分布を計算する方法に係わる。放射線場は中性子およびγ線を含むことができる。本発明の１つの特徴として、原子炉キャビティにおける容器外中性子線量応答を計算することができる。原子炉の型に制限はなく、商用に設計された種々の型に適用できる。好適な原子炉として、例えば、加圧水型原子炉（ＰＷＲ）および沸騰水型原子炉（ＢＷＲ）が挙げられる。説明の便宜上、本発明のこの特徴を２ループの商用ＰＷＲを例に取って説明する。線量応答を発生させるためのＰＷＲのコンピュータ・モデリングはＰＷＲの設計および運転に利用される。 The present invention relates to a method for calculating a radiation field distribution for one system. The radiation field can include neutrons and gamma rays. As one feature of the present invention, the out-of-vessel neutron dose response in the reactor cavity can be calculated. There is no restriction on the reactor type, and it can be applied to various types designed for commercial use. Suitable reactors include, for example, a pressurized water reactor (PWR) and a boiling water reactor (BWR). For convenience of explanation, this feature of the present invention will be described using a two-loop commercial PWR as an example. Computer modeling of the PWR to generate a dose response is used for PWR design and operation.
本発明の方法は、ここではＲＡＰＴＯＲ-Ｍ３Ｇ(RApid Parallel Transport Of Radiation-Multiple 3D Geometries)と呼称する３次元パラレル放射線輸送コードの利用を含む。輸送コードはＳＮ方程式を解くための１組のパラレル・アルゴリズムを提供する。本発明の方法は、空間、角度および/またはエネルギー・ドメインを、マルチプロセッサ・アーキテクチュアに割り振り、それぞれ独立に処理させることが可能なサブセットに分割するドメイン分解アルゴリズムに基づく。公知の好適な３次元パラレル決定論的輸送コードの例としては、ＰＥＮＴＲＡＮＴＭおよびＰＡＲＴＩＳＮ(Sjoden G. E. and Haghighat A., "PENTRAN - Parallel Environment Neutralparticle TRANport in ３次元Cartesian Geometry," Proceedings of the Joint International Conference on Mathematical Methods an Supercomputing for Nuclear Applications, Vol. 1, pp. 232-234, Saratoga Springs, NY(1997))が挙げられる。従来のシングル・プロセッサ方式と比較して、本発明の方法はプロセッサごとの計算負荷および必要メモリを軽減し、大規模な３次元問題に対する効率的な解決方法を提供する。 The method of the present invention, here involves the use of three-dimensional parallel radiation transport codes called RAPTOR-M3G (RA pid P arallel T ransport O f R adiation- M ultiple 3 D G eometries). The transport code provides a set of parallel algorithms for solving the SN equation. The method of the present invention is based on a domain decomposition algorithm that divides the space, angle and / or energy domains into subsets that can be allocated to a multiprocessor architecture and each processed independently. Examples of known preferred 3D parallel deterministic transport codes include PENTTRAN ™ and PARTISN (Sjoden GE and Haghighat A., “PENTRAN-Parallel Environment Neutralparticle TRANport in 3D Cartesian Geometry,” Proceedings of the Joint International Conference on Mathematical Methods an Supercomputing for Nuclear Applications, Vol. 1, pp. 232-234, Saratoga Springs, NY (1997)). Compared with the conventional single processor system, the method of the present invention reduces the calculation load and memory requirement for each processor, and provides an efficient solution to large-scale three-dimensional problems.
ＲＡＰＴＯＲ-Ｍ３Ｇコンピュータ・コードはメッセージ受渡しインターフェース（ＭＰＩ）パラレル・ライブラリを利用してフォートラン９０言語で作成される（Gropp W., Lusk E., and Skjellum A., Using MPI Portable Parallel Programming with the Message Passing Interface, The MIT Press, Cambridge, Massachusetts (1999))。ＲＡＰＴＯＲ-Ｍ３Ｇの幾つかの機能を以下に列記する：
・３次元デカルト・ジオメトリー（ＲＡＰＴＯＲ-ＸＹＺ）および円筒状ジオメトリー（ＲＡＰＴＯＲ-ＲＴＺ）、即ち、不均一な直交格子によるマルチグループＳＮ方程式の解(M. A. Hunter, G. Longoni, and S. L. Anderson, "Extension of RAPTOR-M3G to r-θ-z
geometry for use in reactor dosimetry application," Proceedings of the 13th International Symposium on Reactor Dosimetry, The Netherlands (2008))；
・空間ドメイン、角度ドメインおよび空間/角度結合ドメイン分解アルゴリズム；
・正定値重み付け差分スキーム：ゼロ/θ重み付けおよび方向性θ重み付け；
・２０組またはそれ以下のレベル対称な求積セットの自動的な生成(Longoni G. et al., "Investigation of New Quadrature Sets for Discrete Ordinates Method with Application to Non-Conventional Problems", Transactions of the American Nuclear Society, Vol. 84, pp. 224-226 (2001));
・パラレル・メモリ：空間および角度サブドメインをローカルに割り振ることによって、プロセッサ毎の必要メモリを節減することを可能にする；
・パラレル・タスク：複数のプロセッサでＳＮ方程式を同時に解くことによって、単一のプロセッサを使用する技術と比較して計算時間を短縮する。
・パラレルＩ／Ｏ：それぞれのプロセッサが自らの記憶デバイスにアクセスすることによってＩ／Ｏ時間を短縮する；
・ＢＯＴ３Ｐ(R. Orsi, "Potential Enhanced Performances in Radiation Transport Analysis on Structured Mesh Grids Made Available by BOT3P", Nuclear Science and Engineering, Vol. 157, pp. 110-116 (2007)), 自動格子生成手段、GIPおよびマルチグループ断面積プリプロセッサとの適合性および統合性。
RAPTOR-M3G computer code is written in Fortran 90 language using the Message Passing Interface (MPI) parallel library (Gropp W., Lusk E., and Skjellum A., Using MPI Portable Parallel Programming with the Message Passing Interface, The MIT Press, Cambridge, Massachusetts (1999)). Some features of RAPTOR-M3G are listed below:
3D Cartesian geometry (RAPTOR-XYZ) and cylindrical geometry (RAPTOR-RTZ), ie solutions of multi-group SN equations with non-uniform orthogonal grids (MA Hunter, G. Longoni, and SL Anderson, "Extension of RAPTOR-M3G to r-θ-z
geometry for use in reactor dosimetry application, "Proceedings of the 13th International Symposium on Reactor Dosimetry, The Netherlands (2008));
Spatial domain, angular domain and spatial / angle coupled domain decomposition algorithms;
Positive definite weighting difference scheme: zero / θ weighting and directionality θ weighting;
Automatic generation of 20 or less level symmetric quadrature sets (Longoni G. et al., "Investigation of New Quadrature Sets for Discrete Ordinates Method with Application to Non-Conventional Problems", Transactions of the American Nuclear Society, Vol. 84, pp. 224-226 (2001));
Parallel memory: allows saving memory requirements per processor by allocating spatial and angular subdomains locally;
Parallel task: reduces computation time compared to techniques using a single processor by simultaneously solving SN equations on multiple processors.
Parallel I / O: Each processor accesses its own storage device to reduce I / O time;
・ BOT3P (R. Orsi, "Potential Enhanced Performances in Radiation Transport Analysis on Structured Mesh Grids Made Available by BOT3P", Nuclear Science and Engineering, Vol. 157, pp. 110-116 (2007)), automatic grid generation means, GIP And compatibility and integration with multi-group cross-section preprocessors.
図１aは例えば２ループＰＷＲのような本発明の一実施態様としての３次元輸送モデルの構成を示す。ＰＷＲは１２フィートの炉心、熱遮蔽、および３インチの原子炉キャビティ・エア・ギャップを含むことができる。このモデル構成は炉心−水混合体、炉心シュラウド、炉心バレル、熱遮蔽、ステンレススチール製ライナーを含む原子炉圧力容器（ＲＰＶ）、および反射断熱材を含む。ＰＷＲのＲＰＶはほぼ円筒形に近い形状を呈し、両端が、例えば、下部蓋体および着脱自在な上部蓋体によって閉鎖されている。炉心の上下に位置する上下の内部構造はスチール-水混合体を利用して形成される。ＲＰＶの下部炉心構造は炉心バレル（即ち、炉心支持構造）を含む。炉心バレルはＲＰＶの炉心バレルと内壁との間に設けた熱遮蔽で囲まれている。場合によっては、熱遮蔽の代わりに中性子パッドが使用される。炉心シュラウドは炉心バレルの内側に固定される。環状の降水管が炉心バレルを囲んでいる。冷却流体、典型例としては水が降水管内を循環する。 FIG. 1a shows the configuration of a three-dimensional transport model as an embodiment of the present invention such as a two-loop PWR. The PWR can include a 12 foot core, a heat shield, and a 3 inch reactor cavity air gap. This model configuration includes a core-water mixture, a core shroud, a core barrel, a heat shield, a reactor pressure vessel (RPV) including a stainless steel liner, and reflective insulation. The PWR RPV has a substantially cylindrical shape, and both ends are closed by, for example, a lower lid and a removable upper lid. The upper and lower internal structures located above and below the core are formed using a steel-water mixture. The lower core structure of the RPV includes a core barrel (ie, a core support structure). The core barrel is surrounded by a heat shield provided between the core barrel of the RPV and the inner wall. In some cases, neutron pads are used instead of thermal shielding. The core shroud is fixed inside the core barrel. An annular downcomer surrounds the core barrel. A cooling fluid, typically water, circulates in the downcomer.
図１bは２ループＰＷＲのｚ=０．０ｃｍにおけるｘ−ｙ平面でのモデルの２次元断面を示す。また、ＰＷＲにおける物質の分布をも示す。モデル・ジオメトリーと格子離散化はＢＯＴ３Ｐコード、バージョン５．２を使用して作成する。モデルはｘ−、およびｙ−軸に沿って0.0ｃｍから２４５．０ｃｍ、ｚ−軸に沿って−２００．０ｃｍから２００．０ｃｍまで延びている。モデル全体を通して均一な格子を使用する。ｘ−、ｙ−およびｚ−軸に沿ってそれぞれの格子のサイズを２．０×２．０×４．０ｃｍに規定し、全体として１，４６４，１００個の格子を形成する。 FIG. 1b shows a two-dimensional cross section of the model in the xy plane at z = 0.0 cm of a two-loop PWR. It also shows the distribution of substances in the PWR. Model geometry and grid discretization are created using the BOT3P code, version 5.2. The model extends from 0.0 cm to 245.0 cm along the x- and y-axis and from -200.0 cm to 200.0 cm along the z-axis. Use a uniform grid throughout the model. The size of each grating is defined as 2.0 × 2.0 × 4.0 cm along the x-, y-, and z-axis, and 1,464,100 gratings are formed as a whole.
輸送モデルにおける物質混合体の断面積をＢＵＧＬＥ-９６断面積ライブラリー(RSICC Data Library Collection BUGLE-96,"Coupled 47 Neutron, 20 Gamma-Ray Group Cross Section Library Derived from ENDF/B-VI for LWR Shielding and Pre3ssure Vessel Dosimetry Application," Oak Ridge National Laboratory, Oak Ridge, TN (1999))と、パッケージの一部であるＧＩＰコンピュータ・コード(RSICC Computer Code Collection DOORS 3.2a, "One-, Two- and Three-Dimensional Discrete Ordinates Neutron/Photon Transport Code System," Oak Ridge National Laboratory, Oak Ridge, TN (2003))とを使用して処理する。輸送計算にはＳ８レベル対称求積セットおよび散乱核のＰ３球面調和関
数の展開を利用する。反射断熱材と圧力容器の間の原子炉キャビティ・エア・ギャップに受動型中性子検知器を設けることができる。線量測定システムは原子炉容器の胴回り領域における高速中性子被爆に関して正確な情報を提供することができる。原子炉キャビティには、高速中性子スペクトルのゆがみを最小限に抑制して事実上自由場測定を可能にする、アルミニウム・シェルに封入された純金属フォイルを設けることができる。原子炉キャビティ・エア・ギャップに設置される中性子線量測定器は輸送モデルにおいて明示的に定義されない。
BUGLE-96 cross-section library (RSICC Data Library Collection BUGLE-96, "Coupled 47 Neutron, 20 Gamma-Ray Group Cross Section Library Derived from ENDF / B-VI for LWR Shielding and Pre3ssure Vessel Dosimetry Application, "Oak Ridge National Laboratory, Oak Ridge, TN (1999)) and GIP computer code (RSICC Computer Code Collection DOORS 3.2a," One-, Two- and Three-Dimensional " Discrete Ordinates Neutron / Photon Transport Code System, "Oak Ridge National Laboratory, Oak Ridge, TN (2003)). The transport calculations using the deployment of P 3 spherical harmonics of S 8 level symmetric quadrature set and scattering nuclei. A passive neutron detector can be provided in the reactor cavity air gap between the reflective insulation and the pressure vessel. The dosimetry system can provide accurate information regarding fast neutron exposure in the waist region of the reactor vessel. The reactor cavity can be provided with a pure metal foil encapsulated in an aluminum shell that minimizes the distortion of the fast neutron spectrum and allows virtually free field measurements. Neutron dosimeters installed in the reactor cavity air gap are not explicitly defined in the transport model.
本発明の１つの特徴として、ＳＮ方程式を離散化するためのドメイン分解アルゴリズムが含まれるが、空間および／または角度エネルギー・ドメインをサブセットに分割し、マルチプロセッサ・アーキテクチュアに割り振って独立に処理させる、というアプローチが採用される。 One feature of the present invention includes a domain decomposition algorithm for discretizing the SN equation, but dividing the spatial and / or angular energy domain into subsets and assigning them to a multiprocessor architecture for independent processing. The approach is adopted.
ここに説明するＳＮ方程式の空間および角度離散化も角度ドメイン分解アルゴリズムもコードの３次元デカルト座標ＸＹＺバージョンとって特異である。ＲＡＰＴＯＲ−ＲＴＺのために開発されたＳＮ方程式の公式は散乱再分布項が存在するため，ＲＡＰＴＯＲ−ＸＹＺとは異なる。 Both the spatial and angular discretization of the SN equation and the angular domain decomposition algorithm described here are unique to the three-dimensional Cartesian coordinate XYZ version of the code. The SN equation formula developed for RAPTOR-RTZ differs from RAPTOR-XYZ due to the presence of scattering redistribution terms.
ＳＮ方程式の位相空間は離散化されている、即ち、角度、空間およびエネルギーに離散化されている。従って、結果として得られる線形代数方程式の組はディジタル・コンピュータで解くのに好適である。エネルギー・ドメインは多群アプローチを使用して多数の不連続区間、即ち、最高エネルギー粒子(ｇ＝１)に始まり、最低エネルギー粒子(ｇ＝G)に終わる多数の不連続区間として離散化される。多群近似式における輸送方程式（即ち、ＬＢＥ）は下記方程式（１）で表わされる。
有限の方向組を念頭に、適当な求積積分スキームを適用することによって角度ドメインを離散化する。それぞれの離散方向を、数学的に求積スキームの重みに相当する表面積を有する単位球体の表面上の点として可視化することができる。離散方向と対応の重みとの組み合わせを求積セットと呼称する。一般に、正確且つ数学的に算出可能であるためには、求積セットが多くの条件を満たさねばならず；そのため、幾つかのアプローチ、例えば、レベル対称求積セット（ＬＱｎ）およびルジャンドル多項式に基づく求積セットを利用することができる（Longoni G. and Haghighat A., "Development of New Quadrature sets with the Ordinate Splitting Technique", Proceedings of the ANS International Meeting on Mathematical Methods for Nuclear Applications (M&C 2001), Salt Lake City, UT, September 9-13, 2001, American Nuclear Society, Inc., La Grange Park, IL (2001))。ＲＡＰＴＯＲ‐Ｍ３Ｇにおける求積セットはＬＱｎ法に基づいている。 With a finite set of directions in mind, the angular domain is discretized by applying an appropriate quadrature integration scheme. Each discrete direction can be visualized as a point on the surface of a unit sphere having a surface area that mathematically corresponds to the weight of the quadrature scheme. A combination of the discrete direction and the corresponding weight is called a quadrature set. In general, a quadrature set must satisfy many conditions in order to be accurately and mathematically computable; therefore, it is based on several approaches, for example, a level symmetric quadrature set (LQn) and a Legendre polynomial You can use quadrature sets (Longoni G. and Haghighat A., "Development of New Quadrature sets with the Ordinate Splitting Technique", Proceedings of the ANS International Meeting on Mathematical Methods for Nuclear Applications (M & C 2001), Salt Lake City, UT, September 9-13, 2001, American Nuclear Society, Inc., La Grange Park, IL (2001)). The quadrature set in RAPTOR-M3G is based on the LQn method.
空間変数は有限差分および有限要素法のような幾つかの技術で離散化することができる。ＲＡＰＴＯＲ‐Ｍ３Ｇにおける式は空間ドメインを例えば微細格子のような計算セルに区分し、それぞれのセルの断面積が一定であると想定した有限差分アプローチに基づいている。３次元デカルト幾何学においては、セルの中心位置における角度束が下記方程式（
２）を利用して評価される。
It is evaluated using 2).
上記方程式（２）において、角度およびネルギーの依存性はそれぞれ指数ｍおよびｇで示されている。項ｑi、ｊ、ｋはセル中心における散乱、分裂および外部源の和を表わす。指数ｉ、ｊ、ｋはセル中心の値を表わし、重みai、ｊ、ｋ、ｍ、ｇ、 bi、ｊ、ｋ、ｍ、ｇ、ai、 ci、ｊ、ｋ、ｍ、ｇは０．５から１．０の間に制限される。輸送スイープ中の重みを計算するために、ＲＡＰＴＯＲ‐Ｍ３Ｇはθ重み付け（ＴＷ）、ゼロ重み付け（ＺＷ）、または適当な方向θ重み付け差分スキームを利用する(B. Petrovic and A. Haghighat, "New Directional Theta-Weighted SN Differenｃing Scheme and its Application to Pressure Vessel Fluence Calculations", Proceedings of the 1996 Radiation Protection and Shielding Topical Meeting, Falmouth, MA, Vol. 1, pp. 3-10 (1996))。 In equation (2) above, the dependence of angle and energy is indicated by indices m and g, respectively. The terms q i, j, k represent the sum of scattering, splitting and external sources at the cell center. The indices i, j, k represent cell center values, and weights a i, j, k, m, g, b i, j, k, m, g, a i, c i, j, k, m, g Is limited to between 0.5 and 1.0. To calculate the weights during the transport sweep, the RAPTOR-M3G uses a θ weighting (TW), zero weighting (ZW), or an appropriate direction θ weighting difference scheme (B. Petrovic and A. Haghighat, “New Directional Theta-Weighted S N Differencing Scheme and its Application to Pressure Vessel Fluence Calculations ", Proceedings of the 1996 Radiation Protection and Shielding Topical Meeting, Falmouth, MA, Vol. 1, pp. 3-10 (1996)).
問題のドメインの境界を基点としてそれぞれの方向を辿ることによってＳＮ方程式を解く；この解法は輸送スイープとも呼称される。セル中心位置において画定される角度束は境界の条件または隣接のセルにおいて既に評価された境界角度束から評価される。セル中心角度束は方程式（２）を利用して計算される。計算セルからの角度束は「差分スキーム」と呼称される補足的な関係を利用して計算される。 Solve the SN equation by following each direction from the boundary of the domain in question; this solution is also called a transport sweep. The angle bundle defined at the cell center position is evaluated from the boundary condition or the boundary angle bundle already evaluated in the adjacent cell. The cell center angle bundle is calculated using equation (2). The angle bundle from the calculation cell is calculated using a supplementary relationship called “difference scheme”.
輸送スイープは定点反復法としても知られるソース反復法若しくはリチャードソン反復法と呼称される反復プロセスにおいて実行される。このプロセスは然るべき収束基準が満たされるまで、即ち、ノルムにおけるスカラー束に現れる２つの反復間の相対誤差が所定のカットオフ値以下となるまで続けられる(Adams M. L. and Larsen E. W., "Fast Iterative Methods for Discrete-Ordinates Particle Transport Calculations", Progress in Nuclear Energy, Vol. 40, n. 1 (2002))。放射線遮蔽計算のため、多くの場合、このカットオフ値は1.0e−３または1.0e−４に設定される。 Transport sweeps are performed in an iterative process called source iteration or also known as Richardson iteration, also known as fixed point iteration. This process continues until the appropriate convergence criteria are met, i.e., the relative error between the two iterations appearing in the scalar bundle in the norm is below a predetermined cut-off value (Adams ML and Larsen EW, "Fast Iterative Methods for Discrete-Ordinates Particle Transport Calculations ", Progress in Nuclear Energy, Vol. 40, n. 1 (2002)). For radiation shielding calculations, this cutoff value is often set at 1.0e- 3 or 1.0e- 4 .
ＲＡＰＴＯＲ-Ｍ３Ｇにおけるパラレル・アルゴリズムはプロセッサのネットワーク上に角度および/または空間ドメインを離散させるものである。ＲＡＰＴＯＲ-Ｍ３Ｇは角度および空間ドメインにそれぞれ割り振りされた多数のプロセッサＰaおよびＰsに基づく仮想トポロジーを作成する。離散に必要なプロセッサの総数はＰｎ=Ｐa・Ｐsである。この情報に基づいて、プロセッサのネットワークが空間および角度ドメインにマップされ、それぞれのプロセッサをそのローカル・サブドメインと連携させる仮想トポロジーを作成する。 The parallel algorithm in RAPTOR-M3G discretizes the angular and / or spatial domain on the processor network. RAPTOR-M3G creates a virtual topology based on the angle and number of processors P a and P s, respectively in a space domain are allocated. The total number of processors required for discrete is P n = P a · P s . Based on this information, a network of processors is mapped into the spatial and angular domains, creating a virtual topology that links each processor with its local subdomain.
角度ドメインは８分円ずつに区分され、角度ドメインに特定されたプロセッサが順次ローカル８分円に割当てられる。プロセッサ毎に割当てられる８分円の数は下記方程式（３）によって与えられる。
Ｎloct＝８／Ｐa （３）
The angle domain is divided into eight-yen circles, and the processors specified in the angle domain are sequentially assigned to the local eight-yen circle. The number of octants assigned to each processor is given by equation (3) below.
N loct = 8 / P a ( 3)
輸送スイープはＰaプロセッサにおけるＮloct８分円においてそれぞれ行なわれる；プロセッサ間の角度束を同期化し、境界条件を適正化するために角度ドメインのためのＭＰＩコミュニケーターを使用する。 Transport sweep respectively performed by the N loct 8 quadrants in P a processor; synchronize angle bundle between processors, using the MPI communicator for angle domain in order to optimize the boundary conditions.
Ｐsプロセッサを多数のｘ-ｙ平面に順次割当てるため、ｚ-軸に沿って空間ドメインを区分する。ｚ軸に沿った微細格子の総数、即ち、ｋｍをＰsプロセッサに合わせてそれぞれ区分する；マッピング・アレイ、即ち、ｋｍｌｏｃを利用してｘ-ｙ平面をそれぞれＰsプロセッサに合わせてそれぞれ区分する。Ｐsプロセッサに割当てられるｘ-ｙ平面の数は任意である；但し、問題のジオメトリーと位相的に一致する空間分解を画定するためには、下記方程式（４）の条件が満たされねばならない。
Ｐs
Σ kmloc(i)=km （４）
i=1
In order to sequentially assign the P s processor to multiple xy planes, the spatial domain is partitioned along the z-axis. Partition the total number of fine grids along the z-axis, i.e., km, according to the P s processor; use the mapping array, ie, kmloc, to partition each xy plane according to the P s processor. . The number of xy planes assigned to the P s processor is arbitrary; however, in order to define a spatial resolution that topologically matches the geometry in question, the condition of equation (4) below must be met.
Ps
Σ kmloc (i) = km (4)
i = 1
空間ドメインに割当てられたプロセッサを任意数のｘ-ｙ平面にマップできるフレキシビリティはｚ平面の数が空間ドメインに割当てられたプロセッサの数によって割り切れるかどうかに依存する。Ｐsプロセッサに対してｘ-ｙ平面を不均一に区分すると、プロセッサ負荷のアンバランスを招き、結果として性能損失に陥る。本発明では、ハイブリッド角度/空間分解ストラテジーを適用することによってこの難題を克服することができる。ハイブリッド分解は角度および空間ドメインを組み合わせることによって両ドメインが並行区分されるようにする。ハイブリッドドメイン分解については、実施例１においてさらに詳しく後述する。 The flexibility to map a processor assigned to the spatial domain to any number of xy planes depends on whether the number of z planes is divisible by the number of processors assigned to the spatial domain. If the xy plane is divided unevenly with respect to the P s processor, the processor load is unbalanced, resulting in a performance loss. In the present invention, this challenge can be overcome by applying a hybrid angular / spatial decomposition strategy. Hybrid decomposition allows both domains to be partitioned in parallel by combining angular and spatial domains. Hybrid domain decomposition will be described in more detail later in Example 1.
図５は３次元放射線輸送コンピュータ・プログラムを実行することによって放射線場分布を作成する本発明の一実施態様のフローチャートを示す。この実施態様はモデリングすべきシステムにおける幾何的情報および材料情報を得るステップを含む。情報は、例えば、原子炉設計図のような種々の情報ソースから入手することができる。次いで、計算に必要な充分なＳＮ方程式の階数を選択する。さらに、角度ドメイン（即ち、散乱核および角度束）に対するＰn拡張の程度を選択する。適当な差分スキーム（即ち、ＴＷ、ＺＷまたはＤＴＷ）も選択することができる。デカルト座標ＸＹＺまたはＲＴＺジオメトリーのための適当な格子生成手段を利用してシステムの３次元モデルを生成することができる。例えば、ＢＵＧＬＥ-９６のような適当なデータセットと混合することによって材料毎に断面積表を作成する。プロセッサの数およびこれに対応の分解ストラテジーは、解くべき問題に合わせて選択される。次いで、計算を実行する。計算に続いて、後処理および結果分析を行う。 FIG. 5 shows a flowchart of one embodiment of the present invention for creating a radiation field distribution by executing a three-dimensional radiation transport computer program. This embodiment includes obtaining geometric information and material information in the system to be modeled. Information can be obtained from a variety of information sources, such as, for example, a reactor blueprint. Then, select a sufficient rank of the SN equation necessary for the calculation. In addition, the degree of P n expansion for the angular domain (ie, scattering nuclei and angular bundles) is selected. An appropriate difference scheme (ie TW, ZW or DTW) can also be selected. A suitable grid generation means for Cartesian coordinates XYZ or RTZ geometry can be used to generate a three-dimensional model of the system. For example, a cross-section table is created for each material by mixing with an appropriate data set such as BUGLE-96. The number of processors and the corresponding decomposition strategy are selected according to the problem to be solved. The calculation is then performed. Following the calculation, post-processing and results analysis are performed.
本発明に使用されるＲＡＰＴＯＲ-Ｍ３Ｇコンピュータ・コードは放射線輸送の問題を正確且つ効率的に（例えば、計算時間の短縮）解くことを可能にする。本発明の１つの特徴として、原子炉容器キャビティに関して、容器外中性子線量応答を計算する。実測値と比較して，ＲＡＰＴＯＲ-Ｍ３Ｇによって計算された２ループＰＷＲの原子炉キャビティ・エアギャップにおける高速中性子反応は平均して９６％の精度を示した。また、ハイブリッド角度/空間ドメイン分解ストラテジーを利用する２０個のプロセッサによるコンピュータ・クラスタでは輸送問題の解が約１０６分間で得られた。 The RAPTOR-M3G computer code used in the present invention allows the problem of radiation transport to be solved accurately and efficiently (eg, reduced computation time). As one feature of the present invention, an out-of-vessel neutron dose response is calculated for the reactor vessel cavity. Compared with the measured values, the fast neutron reaction in the reactor cavity and air gap of the two-loop PWR calculated by RAPTOR-M3G showed an accuracy of 96% on average. Also, a 20 cluster computer cluster utilizing a hybrid angular / space domain decomposition strategy provided a solution to the transport problem in about 106 minutes.
本発明の特定の実施態様を詳細に亘って以上に説明したが、当業者には明らかなように、開示した内容に照らして、細部に種々の変更を加えることができる。例えば、原子力産業、特に、原子炉に関連して本発明の特徴を説明した。しかし、本発明は医療分野のような他の分野にも広く利用することができる。例えば、癌治療のため患者に照射すべき放射線量を測定する目的に利用することができる。従って、開示した特定の構成はあくまでも説明のためのものであって発明の範囲を制限するものではなく、発明の範囲は後記する請
求の範囲およびその均等物によって与えられる。
While specific embodiments of the present invention have been described above in detail, it will be apparent to those skilled in the art that various changes can be made in detail in light of the disclosure. For example, the features of the present invention have been described in the context of the nuclear industry, in particular, nuclear reactors. However, the present invention can be widely used in other fields such as the medical field. For example, it can be used for the purpose of measuring the radiation dose to be irradiated to a patient for cancer treatment. Accordingly, the specific configuration disclosed is for illustrative purposes only and does not limit the scope of the invention, which is provided by the following claims and their equivalents.
実施例１−ＲＡＰＴＯＲ-Ｍ3Ｇパラレル性能分析Example 1-RAPTOR-M3G Parallel Performance Analysis
以下に述べる実施例における輸送計算は２０プロセッサによるコンピュータ・クラスタ、即ち、ＥＡＧＬＥ-１で運用されるＲＡＰＴＯＲ-Ｍ３Ｇで行なわれた。このクラスタは２デュアルコア・デュアル・プロセッサＡＭＤ Ｏｐｔｅｒｏｎによる６４-ビットのアーキテクチュアを有する５つのノードから構成された。利用可能なクラスタ・トータル・メモリ、即ち、ＲＡＭは４０ギガバイト；ネットワーク相互接続は1 ギガビット／秒の帯域幅を特徴とするものであった。このようなハードウェア構成で、ＲＡＰＴＯＲ-Ｍ３Ｇは２ループＰＷＲのための全３次元輸送計算を２０のプロセッサによって約１０６分間で完了した。ＤＴＷ，ＴＷ，またはＺＷ差分スキームを使用しても、性能に目立った差は観察されなかった。 The transport calculations in the examples described below were performed on a 20-processor computer cluster, ie, RAPTOR-M3G operating on EAGLE-1. This cluster consisted of 5 nodes with 64-bit architecture with 2 dual core dual processors AMD Opteron. Available cluster total memory, or RAM, was 40 GB; the network interconnect was characterized by a bandwidth of 1 gigabit / second. With such a hardware configuration, the RAPTOR-M3G completed the full three-dimensional transport calculation for the two-loop PWR in about 106 minutes with 20 processors. Using the DTW, TW, or ZW difference scheme, no noticeable difference in performance was observed.
さらにまた、コードのパラレルな性能を分析するため、簡単な試験問題を設定した。試験問題として、均一に分布された固定発生源を有し、１ｃｍの均一な格子で離散化された５０´５０´５０のボックスを使用した。Ｓ８求積セットおよびＰ０等方性散乱を１エネルギー群断面積群と併用した。柱時計時間、スピードアップおよびパラレル効率を、ＲＡＰＴＯＲ−Ｍ３Ｇのパラレル効率の評価に利用した。スピードアップおよびパラレル効率はそれぞれ方程式５および６によって定義した。
Ｓｐ=Ｔs/Ｔp （５）
hp=Ｓp/Ｎp （６）
上記式において、ＴsおよびＴpはそれぞれシングル・プロセッサおよびマルチプロセッサが必要とする柱時計時間を表わす。Ｎpは柱時計時間Ｔpを達成するために利用されるプロセッサの数を表わす。図４はそれぞれ異なる分解ストラテジーを採用した場合に、２０基までのプロセッサで得られるスピードアップの比較を示す。
In addition, a simple test question was set up to analyze the parallel performance of the code. As a test problem, we used 50'50'50 boxes with uniformly distributed stationary sources and discretized with a 1 cm uniform grid. The S 8 quadrature set and P 0 isotropic scattering in combination with 1 energy group cross area group. Wall clock time, speedup and parallel efficiency were used to evaluate the parallel efficiency of RAPTOR-M3G. Speedup and parallel efficiency were defined by equations 5 and 6, respectively.
S p = T s / T p (5)
h p = S p / N p (6)
In the above equation, T s and T p represent wall clock times required by a single processor and a multiprocessor, respectively. N p represents the number of processors used to achieve the wall clock time T p . FIG. 4 shows a comparison of speedups obtained with up to 20 processors with different disassembly strategies.
空間分解で得られるスピードアップはプロセッサの数が増えるに従って次第に低下した。この挙動はプロセッサごとの計算細分性が増すため、と考えられる；空間ドメインがより小さいサブドメインに分解されるから、プロセッサごとの動作数が増える一方で、プロセッサ間の通信時間が増大した；従って、性能が低下する。ノード間のネットワーク・データ伝送は分散メモリ・アーキテクチュアにおける制限要因となるのが普通であった。問題を収束するのに必要な反復回数が多くなると、これが空間分解ストラテジーの性能を低下させる要因となった。しかし、角度ドメインと空間ドメインを同時的に区分するハイブリッド分解は好ましい結果をもたらした。この好ましい挙動はこの分解によって生ずる計算細分性が比較的粗いためと考えられる；また、ハイブリッド分解の場合、問題を収束するのに必要な反復数は空間分解の場合ほど多くはならなかった。 The speedup gained by spatial decomposition gradually decreased as the number of processors increased. This behavior is thought to be due to increased computational granularity per processor; since the spatial domain is broken down into smaller subdomains, the number of operations per processor increases while communication time between processors increases; , Performance decreases. Network data transmission between nodes has typically been a limiting factor in distributed memory architectures. As the number of iterations required to converge the problem increased, this became a factor in reducing the performance of the spatial decomposition strategy. However, hybrid decomposition that simultaneously partitions angular and spatial domains has yielded favorable results. This favorable behavior is believed to be due to the relatively coarse computational granularity produced by this decomposition; and in the case of hybrid decomposition, the number of iterations required to converge the problem was not as great as in the case of spatial decomposition.
実施例２−ＲＡＰＴＯＲ-Ｍ３Ｇ計算応答との実測線量応答の比較Example 2-Comparison of measured dose response with RAPTOR-M3G calculated response
実測線量応答と、ＲＡＰＴＯＲ-Ｍ３Ｇで得られる対応の予測とを比較した。ＩＲＤＦ-２００２Ｄｏｓｉｍｅｔｒｙ Ｌｉｂｒａｒｙ(I. Kodeli and A. Trkov, "Validation of the IRDF-2002 Dosimetry Library", Nuclear Instruments and Method in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 57, Issue 3, pp. 664-681 (2007))を使用して表１に示す中性子反応に対する線量応答の計算値を求めた。 The measured dose response was compared with the corresponding prediction obtained with RAPTOR-M3G. IRDF-2002 Dosimetry Library (I. Kodeli and A. Trkov, "Validation of the IRDF-2002 Dosimetry Library", Nuclear Instruments and Method in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 57, Issue 3, pp. 664-681 (2007)), the calculated dose response values for the neutron reactions shown in Table 1 were obtained.
表１に示す反応に対応する線量応答の実測値を、ＲＡＰＴＯＲ−Ｍ３Ｇによる応答計算値と比較した。 The measured values of the dose response corresponding to the reactions shown in Table 1 were compared with the response calculated by RAPTOR-M3G.
表１．線量測定システムによって測定される中性子反応
物質 反応
銅 ６３Cu(ｎ，α)６０Co
鉄 ５４Fe(ｎ，p)５４Mn
ニッケル ５８Ni(ｎ，ｐ)５８Co
ウラニウム ２３８U(ｎ，ｆ)１３７Cs
ネプツニウム ２３７Np(ｎ，ｆ)１３７Cs
Table 1. Neutron reaction measured by dosimetry system Material reaction Copper 63 Cu (n, α) 60 Co
Iron 54 Fe (n, p) 54 Mn
Nickel 58 Ni (n, p) 58 Co
Uranium 238 U (n, f) 137 Cs
Neptunium 237 Np (n, f) 137 Cs
表1に示す反応は、カドミウム遮蔽金属フォイルを使用して測定した；従って、中性子スペクトルの熱成分は抑制された。 The reactions shown in Table 1 were measured using a cadmium shielding metal foil; therefore, the thermal component of the neutron spectrum was suppressed.
応答の実測値を４箇所、即ち、原子炉キャビティ・エア・ギャップの炉心中央平面における０°、１５°、３０°、および４５°において求めた。２ループＰＷＲは核燃料とＲＰＶとが近接しているため、０°位置に高速中性子フルエンスのピークがあるのが特徴であり、これを考慮してこの位置では追加測定を行なった。即ち、０°位置では活性炉心の軸方向頂部と底部とで実測値を求めた。線量応答の計算値は一貫して実測値を過大に予測させる、との所見を得た。 The measured response values were determined at four locations, namely 0 °, 15 °, 30 °, and 45 ° in the core midplane of the reactor cavity air gap. Since the two-loop PWR is close to the nuclear fuel and the RPV, the fast neutron fluence peak is at the 0 ° position, and additional measurements were performed at this position in consideration of this. That is, at the 0 ° position, measured values were obtained at the top and bottom in the axial direction of the active core. It was found that the calculated dose response consistently overestimates the actual measurement.
さらに検討した結果、輸送モデルに使用されたＲＰＶの厚さが原子炉圧力容器（ＲＰＶ）の稼動時点検（ＩＳＩ）時に測定された厚さよりも薄かったことが判明し、初期の所見が裏付けられた。輸送モデルに新しいＲＰＶ厚さを採用した結果、線量計算値データの精度が平均して８％だけ改善された。線量測定の実測値とＤＴＷ適応差分スキームを利用して計算された計算値との比（Ｍ/Ｃ）を図２に示す。 Further investigation revealed that the RPV thickness used in the transport model was thinner than the thickness measured during the in-service inspection (ISI) of the reactor pressure vessel (RPV), confirming the initial findings. It was. As a result of adopting a new RPV thickness for the transport model, the accuracy of the calculated dose data improved by an average of 8%. FIG. 2 shows the ratio (M / C) between the measured value of the dose measurement and the calculated value calculated using the DTW adaptive difference scheme.
図２に示すように、いずれの位置においても、またいずれの線量被測定物質においても、Ｍ/Ｃ比は一貫して１０％の範囲内であった。３０°および４５°方位角位置における過大予測は、システムの湾曲がより適正になるようにこれらの位置を不均一格子で修正することによって軽減することができた。すべての線量測定箇所の平均Ｍ／Ｃ比は０．９６であった。 As shown in FIG. 2, the M / C ratio was consistently within a range of 10% at any position and at any dose measurement substance. Overestimation at 30 ° and 45 ° azimuthal positions could be mitigated by correcting these positions with a non-uniform grid so that the curvature of the system would be more appropriate. The average M / C ratio at all dose measurement points was 0.96.
図３a乃至３cはＲＰＶの厚さをＩＳＩ修正して得たＭ/Ｃ値を、厚さ修正無しで得られた値と比較して示す。この比較は０°方位各位置のすべての線量測定試料に関して実施されたものである。ＩＳＩ測定を利用して修正されたＲＰＶ厚さはすべての線量測定部位における応答計算値の精度を改善した。１５°、３０°、および４５°方位角位置においても同様の結果が得られた。 Figures 3a to 3c show the M / C values obtained by ISI correction of the RPV thickness compared to the values obtained without thickness correction. This comparison was performed for all dosimetry samples at each position in the 0 ° azimuth. RPV thickness modified using ISI measurements improved the accuracy of response calculations at all dosimetry sites. Similar results were obtained at 15 °, 30 °, and 45 ° azimuthal positions.
それぞれの線量測定箇所における反応率の実測値および計算値と、ＩＳＩ測定値で修正されたＲＰＶの厚さで得られたＭ/Ｃ比を図２に示した。表２に示す反応に関連の平均Ｍ／Ｃ比はすべての線量測定箇所に亘って０．９６であった。 FIG. 2 shows the M / C ratio obtained from the measured and calculated values of the reaction rate at each dose measurement location and the thickness of the RPV corrected with the ISI measurement values. The average M / C ratio associated with the reactions shown in Table 2 was 0.96 across all dosimetry sites.
表２．ＤＴＷ差分スキームで得られた反応率の測定値および計算値Table 2. Measured and calculated reaction rates obtained with the DTW difference scheme
Claims (20)
角度ドメインおよび空間ドメインからなる群から選択されたドメインを含むドメイン分解アルゴリズムから成る３次元放射線輸送コンピュータ・コードを適用するステップより成り、前記ドメインはマルチプロセッサ・コンピュータ・アークテクチュアに割り振り、処理されることを特徴とする放射線場分布の計算方法。 A method for calculating the distribution of radiation fields,
Applying three-dimensional radiation transport computer code comprising a domain decomposition algorithm comprising a domain selected from the group consisting of an angular domain and a spatial domain, wherein the domain is allocated and processed in a multiprocessor computer architecture. A method of calculating a radiation field distribution, characterized by:
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| CN104678424A (en) * | 2013-12-03 | 2015-06-03 | 中广核（北京）仿真技术有限公司 | Neutron counting system and method for nuclear power plant analog machine |
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