KR101206368B1 - Method of assignment of partial slip condition at solid boundaries in numerical modeling of two-dimensional shallow water - Google Patents

Abstract

The present invention relates to a method for imparting partial activity conditions to a solid boundary surface in a two-dimensional shallow water numerical modeling, wherein (a) the central processing unit is configured to satisfy certain equations by using a program in a main memory including certain equations. Calculating and storing tangent and normal vectors at the boundary plane in the coordinate system; (b) inputting, by the input device, the hydrostatic pressure initial condition to which the zero flow rate and the constant depth are given to all nodes including the boundary nodes; (c) identifying a node of a solid boundary surface in the topographic information file and storing the boundary node and the length of action (b) in the main memory by the input device; (d) The central processing unit satisfies certain equations using a program in the main memory including the input data and certain equations, using the tangent and normal vectors, the initial condition of hydrostatic pressure, and the length of activity (b) as input data. Calculating and storing the flow rate at the boundary node by applying the partial activity condition; and (e) using the initial hydrostatic pressure condition and boundary condition as input data, the central processing unit uses the finite element method for the input data and certain equations. This method consists of calculating and storing longitudinal flow velocity and depth at any time and location satisfying certain equations using a program in the numerically modeled main memory, thereby more accurately interpreting shallow water flow in natural rivers. It is possible to provide a method for analyzing the shallow water flow with improved accuracy, applicability, and reliability.

Description

Method of assignment of partial slip condition at solid boundaries in numerical modeling of two-dimensional shallow water}

The present invention relates to a method for imparting partial activity conditions to a solid boundary surface in two-dimensional shallow water flow numerical modeling. Water flow in rivers can be more accurately analyzed, and the boundary conditions on the wall can be generalized to partial activity conditions, enabling the application of both full and inactive conditions, and improving water flow with improved accuracy, applicability and reliability. It is about how to interpret.

In general, when analyzing the flow of a real fluid rather than an ideal fluid, friction shear stress is generated by the viscous effect of the fluid, and there is a boundary layer (boundary layer) that is an area affected by such friction.

In particular, when the actual fluid flows around the obstacle, separation may occur because the wireline may not turn sharply at the rear of the interface due to the inertia force. In order to accurately predict the frictional shear stress and the delamination caused by the solid structure present in the fluid flow, an assumption about the fluid motion at the interface is required.

In addition, in order to simulate free surface flow in hydrodynamics, hydraulics, and hydrodynamics, mass conservation equations and momentum conservation equations are applied by applying the laws of physics based on the continuum hypothesis. This equation is generally expressed as a nonlinear partial differential equation, and in general, there is no interpretation solution for it, so computer-based digitization is widely used to solve it.

However, the boundary condition is necessary to terminate a given governing equation. Especially, the boundary condition imparted to the solid interface changes the shear force distribution at the interface and thus has a very important influence on the degree of separation of the flow. In addition, the wall boundary condition is directly related to the development of turbulence inducing turbulence (Niavarani and Priezjev, 2009), which is the most important factor in analyzing the flow field near the solid interface. Therefore, the assumption of fluid motion at the physical interface is very important in hydrodynamic flow analysis.

The flow velocity of the fluid at the solid interface can be divided into normal and tangential components. From a physical point of view, the fluid cannot pass through the solid wall, so the impermeable condition of zero normal flow velocity perpendicular to the interface is intuitive.

On the other hand, the existence of tangential flow rate components has been debated since the early days of hydrodynamics and the relative velocity of fluid at the interface between solid and fluid contact by fluid mechanics in the late 18th and early 19th centuries. A no-slip condition of 0 was conventionally accepted. This hypothesis, however, is not driven by basic laws of physics, but by long-term tacit agreements, and because of recent rapid advances in observational equipment and technology, there is a weak non-zero flow rate in the tangential direction at the solid interface. (Tophøj et al., 2006; Hron et al., 2008; Daniello et al., 2009; Liu et al., 2009; Niavarani and Priezjev, 2010).

Indeed, the tangential flow velocity of the solid boundary exists not only in microflows but also in low-viscosity flows, fluid flows through chemically treated walls, high shear flows, and when submerged objects are submerged in water. As a result, inactivation conditions conventionally applied are not established. The drag is generated by the shear force caused by the difference between the upstream flow rate and the flow velocity around the solid interface. In various fields of fluid engineering, much effort is being made to reduce the magnitude of the force, especially in the solid surface In the case of hydrophobic coating, the flow velocity is generated at the interface, and the drag is greatly reduced. Therefore, even in order to reduce the drag, partial analysis can be used for accurate analysis.

However, the existing two-dimensional water flow analysis model at home and abroad does not accurately consider the magnitude of the flow velocity at the boundary of the structure, but simply analyzes the flow of the fluid using free-slip or inactive conditions. The direction and magnitude of flow velocity in Esau, the rise and fall of the water level, the distribution of shear force, the change of drag force and lift force over time have not been correctly interpreted, and the flow behavior and difference in natural rivers There is a problem that seems.

The present invention has been made to solve the above problems, and an object of the present invention is to develop a finite element model that can accurately predict the horizontal two-dimensional flow velocity distribution (flow field, flow characteristics, etc.) around the structure, and this model We propose a method of applying partial-slip conditions to more accurately interpret complex flow structures in the model, and propose a method that can include full, partial and inactive conditions for accuracy and application. The present invention provides a method for imparting partial activity conditions to a solid boundary surface in two-dimensional shallow water flow numerical modeling, which can analyze the shallow water flow with improved performance and reliability.

Another object of the present invention is to analyze the flow velocity, depth distribution and vortex around the structure according to the slip length, and to input all the full, partial and inactive conditions by changing the length of activity. By presenting a method of imparting partial activity condition to solid boundary surface in 2D shallow water numerical modeling, which can analyze the difference of shallow water flow according to the application of wall boundary conditions.

To achieve these and other advantages and in accordance with the purpose of the present invention,

(a) The central processing unit uses a program in the main memory containing the following equations, that is,

와

Wow

와

는 각각 경계절점 C에서의 형상함수

의 x와 y방향으로의 편미분)을 만족하는 자연좌표계에서 경계면에서의 접선(-n_y,n_x) 및 법선벡터(n_x,n_y)를 계산 저장하는 단계와;Where I, II, and III are elements containing boundary nodes C, and dA is the area of this element,

Wow

Are the shape functions at boundary node C, respectively.

Calculating and storing a tangent (-n _y , n _x ) and a normal vector (n _x , n _y ) at an interface in a natural coordinate system satisfying the partial differential in x and y directions of;

(b) inputting, by the input device, the hydrostatic pressure initial condition to which the zero flow rate and the constant depth are given to all nodes including the boundary nodes;

(c) identifying a node of a solid boundary surface in the topographic information file and storing the boundary node and the length of action (b) in the main memory by the input device;

(d) The central processing unit uses the program in the main memory including the input data and the following equations using the tangent and normal vectors, the hydrostatic initial conditions and the active length as input data. , In other words,

와

Wow

(Where b is the active length, n _x and n _y are the x- and y-direction components of the normal unit vector at the interface, respectively, u ₁ and u ₂ are the longitudinal and horizontal flow rates respectively). Calculating and storing the flow rates u _s1 and u _s2 at the boundary node by the edge node, and

(e) Using the initial hydrostatic pressure condition and boundary condition (upstream flow velocity, downstream depth, flow velocity at boundary node), the central processing unit inputs the input data (initial hydrostatic pressure condition and boundary condition) and The finite element method is applied to the equations so that the following equations, i.e.

,

,

와

Wow

(Where, h is the water depth, u ₁ and u ₂ are respectively the vertical and horizontal directions depth mean velocity, g is the distance, ν _T of the acceleration of gravity, n is the number of roughness indicating the roughness degree of the bed and the wall, to the charge image H is from the reference line is Comprising a step of calculating and storing longitudinal flow velocity (excluding boundary node) and water depth (including boundary node) at any time and location satisfying the eddy viscosity.

In addition, the present invention again reflects the calculated flow field (vertical flow velocity and depth) obtained when the change amount Δu ₁ , Δu ₂ , Δh of the result calculated in step (e) is larger than the allowable range of 10 ^−5. In order to calculate the partial activity condition and reflect the boundary condition, the flow fields converged repeatedly (u ₁ , u ₂ , h) until the process of steps (d) and (e) are re-run and smaller than the allowable range. It characterized in that it further comprises the step of obtaining.

In the existing domestic and foreign two-dimensional water flow analysis model, the fluid flow is analyzed near the structure by using the free-slip condition or the no-slip condition, ignoring the flow velocity generated at the boundary of the structure. The direction and magnitude of flow velocity, the rise and fall of the water level, the distribution of shear force, and the change of the drag and lift over time were not interpreted correctly, resulting in differences in the flow behavior in natural rivers. However, in the above-described two-dimensional shallow water flow numerical modeling, the method of imparting partial activity conditions to the solid boundary surface is applied to the boundary surface in the process of applying the finite element model to the two-dimensional shallow water equation. The method of analyzing the shallow water flow with improved accuracy, applicability and reliability by analyzing the shallow water flow more accurately and generalizing the boundary condition on the wall as a partial activity condition so that it is possible to apply both the full and inactive conditions. There is an effect that can provide.

1 is a diagram illustrating a numerical simulation flow chart for applying partial activity conditions in accordance with the present invention.
2 is a diagram illustrating discrete boundary planes and normal unit vectors for defining a shape function.
3 shows the flow rate component at the active length (b) and the interface.
4 shows a finite element grid for applying partial activity conditions.
5 is a view showing a flow field comparison (left: b = ∞, right: b = 0.0) according to the activity length.
6 is a view showing a longitudinal flow rate distribution in the vicinity of a structure according to various activity conditions.
7 is a diagram showing a lateral flow velocity distribution near a structure according to partial activity conditions.
8 is a view showing the change pattern of the flow rate component in the back of the structure over time.
9 is a view showing the change pattern with time of eddy at the rear of the structure.
10 is a diagram showing a eddy distribution comparison (solid line: b = 0.0, dotted line: b = 3.0 mm).
11 shows the flow rate distribution at the boundary of a structure.
12 shows the water distribution at the boundary of the structure.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.

Most existing domestic and foreign commercial models such as RMA-2, Telemac-2D, and River2D calculated flow fields assuming a free-slip condition as the boundary condition at the river structure as the inner boundary and the side wall as the outer boundary. In practice, however, it is physically valid for partial activity conditions where the flow is weak due to friction at the solid interface.

Therefore, the present invention uses a governing equation such as Equation 1 to Equation 3 below to present a method for analyzing two-dimensional shallow water flow using partial activity conditions.

Where h is depth, u ₁ and u ₂ are longitudinal depth mean velocity, g is gravitational acceleration, n is roughness coefficient representing roughness of bed and wall, H is distance from baseline to ν _T Indicates the viscosity coefficient. In the present invention, the equation 1, which is a mass conservation equation, is discretized by the Galerkin method, the equations 2 and 3, which are momentum conservation equations, by the SU / PG method.

Consideration of irregular boundary and wall boundary condition

For flow analysis in rivers and waterways, wall boundary conditions apply to the left eye, right eye, and internal structures. In the finite element model, the velocity components at the inner and outer boundaries are calculated by dividing them into tangential and normal directions. In the case of the terrain as shown in FIG. 2, in order to obtain the flow velocity component at the boundary node C point, the shape function of the element including the boundary node C as shown in Equations 4 and 5 is considered The x-direction component (n _x ) and the y-direction component (n _y ) of the normal unit vector are first calculated.

와

는 각각 경계절점 C에서의 형상함수

의 x와 y방향으로의 편미분을 의미한다.Where I, II and III are elements (see Fig. 2) each containing boundary node C, and dA is the area of this element,

Wow

Are the shape functions at boundary node C, respectively.

Means the partial derivative in the x and y directions.

Using this, the flow velocity (u ₁ , u ₂ ) and the flow velocity (u _n , u _t ) in the Cartesian coordinate system at the boundary node C can be expressed as in Equations 6 and 7 below.

Where u _n Is the normal flow rate, u _t Is the tangential flow rate.

Therefore, in the case of using the active condition in which the tangential flow velocity on the wall exists, u _n in Equation 6 = 0 if the grant is applied to both the tangential and the normal direction of flow rates 0 muhwal condition of the wall is u = u _{t n} = 0 is applied. Partial activity conditions are imparted by the methods detailed below.

Water Flow Analysis  Of subactivities in computer models

성분은 접선점성응력(tangential viscous stress) 및 활동길이(b)에 비례한다는 것으로 다음의 수학식 8과 같이 나타낼 수 있다.As described above, it has been found that there is a nonzero tangential flow rate in the tangential direction at the solid interface, where the tangential flow rate at this solid surface is described as partial activity conditions. This condition is the tangential flow rate

The component is proportional to the tangential viscous stress and the length of activity (b) and can be expressed as in Equation 8 below.

와

는 경계면에서 수직 및 평행한 단위벡터 (도 3 참조), ν_T 는 동점성계수,

는 고체경계면에서의 직교좌표계 방향 유속, b 는 도 3과 같이 경계면에서부터 수직인 방향으로 외삽에 의해 0이 되는 유속이 존재하는 지점까지의 거리로 정의되는 활동길이이다. 접선점성응력(

)은 다음의 수학식 9와 같이 정의된다.here,

Wow

Is the unit vector vertical and parallel at the interface (see Fig. 3), ν _T is the kinematic viscosity,

Is the flow velocity in the Cartesian coordinate system direction at the solid boundary surface, and b is the action length defined as the distance from the boundary surface to the point where the flow velocity becomes zero by extrapolation in the vertical direction. Tangential Viscous Stress

) Is defined as in Equation 9 below.

Equation 10 is used to impart an impermeable condition that no flow rate penetrates the interface.

Equations 8 and 10 can be solved and written as in Equations 11 and 12 below.

조건을 이용하여 이 두 식을 더하면 경계면에서의 x-방향 접선유속성분(u_s1)은 다음의 수학식 13과 같이 표현된다.Multiply n _y and n _x by Equations 11 and 12, respectively.

Adding these two equations using the condition, the x-direction tangential velocity component u _s1 at the interface is expressed by Equation 13 below.

Similarly, the y-direction tangential flow rate component u _s2 at the interface is expressed by Equation 14 below.

The larger the active length (b), the smaller the frictional force at the interface and the greater the flow velocity at the interface. Full activity conditions and inactive conditions are special cases of partial activity conditions. When activity length is 0, it becomes inactive condition and when activity length is infinite, it becomes full activity condition. In general CFD modeling, sidewalls are assigned full activity conditions, while other interfaces are assigned inactive or partial activity conditions. This is because when the inactive condition is input to the side wall, singularity is generated between the node located on the wall and the adjacent internal node, a sudden flow change occurs and the flow is excessively distorted.

On the other hand, the numerical simulation process for applying the partial activity conditions as shown in Figure 1 using the boundary conditions and the partial activity conditions as follows.

First, the central processing unit transforms the coordinate axes into natural coordinates by means of iso-parametric elements, and then tangents (-n _y , n _x ) and normal vectors (n _x , n _y ) at the interface. ) Is calculated and stored using a program in the main memory including Equations (4) and (5). In this case, the transformation to the natural coordinate system is performed by a program coding an algorithm directly through a programming language in order to perform this by a computer (S10).

Next, a hydrostatic initial condition in which all the nodes including the boundary node are given a flow rate of zero and a constant depth is input to the main memory by the input device (S20).

Next, the node of the solid boundary surface is identified from the topographic information file, and the boundary node and the action length (b) are input and stored in the main memory by the input device (S30).

Next, the central processing unit uses the program in the main memory including the equations (13) and (14) to apply the partial activity condition using the tangent and normal vectors, the hydrostatic initial conditions and the active length (b) as input data. Allocating and storing the flow rate at the boundary node (S40).

Next, the node to which the boundary condition is assigned has a known value (flow velocity at the boundary node; u _s1 , u _s2 ) by the degree of freedom constrained, so it is excluded from the solution of the governing equation and adjacent. It modifies the load vector of the node. Therefore, the central processing unit uses the initial hydrostatic pressure conditions and boundary conditions (upstream flow velocity, downstream depth, flow velocity at the boundary node) as input data, and the central processing unit determines the input data (initial hydrostatic pressure condition and boundary conditions) and the governing equation. The longitudinal flow velocity (excluding boundary node) and depth at any time and location satisfying Equations 1 to 3 using a program in a numerically modeled main memory by applying the finite element method to Equations 1 to 3 above. (Including the boundary node) is calculated (S50). For reference, the numerical model is a program in which an algorithm is directly coded through a programming language (Fortran, etc.) to be finally executed by a computer.

Finally, if the amount of change (Δu ₁ , Δu ₂ , Δh) of this result is larger than the allowable range (preferably 10 ^-5 ), the partial activity condition is calculated again to reflect the calculated flow field (vertical flow velocity and depth). In order to reflect the boundary condition, the flow fields (u ₁ , u ₂ , h) are repeatedly obtained until the processes of steps S40 and S50 are performed again and smaller than the allowable range.

Flow analysis applying partial activity conditions

In the present invention, in order to analyze the flow velocity, water level, and vortex distribution around the internal structure according to the fully active condition, the partial activity condition, and the inactive condition without the flow velocity on the wall, The same numerical simulation conditions were constructed.

The channel width and length are 2m and 4m, respectively, with the diameter of the structure (D) 0.22 m, the upstream flow velocity (u _∞ ) 0.1 m / s, the downstream depth (h _∞ ) 0.5 m, the coarseness ^coefficient 0.012 m ^-1/3 ? The Re number, a dimensionless number defined by the ratio of s, the inertia force and the viscous force, constituted a condition of 100. The magnitude of the velocity at the interface is determined by the length of action (b), which means full activity conditions for b = ∞, inactive conditions for b = 0.0, and partial activity conditions for other values. Considered. The grid for numerical simulation is composed of 1,912 nodes and 1,835 triangular and rectangular meshes as shown in FIG. 4, and a dense grid is constructed near the wall to reproduce the partial activity conditions more accurately.

The flow field calculated by the numerical simulation conditions of Table 1 is shown in FIG. 5. 5 is to show the change pattern of the velocity field according to the active length set to the complete and inactive conditions. FIG. 5 (a) shows the velocity vector diagram, and in the case of b = ∞ (completely active condition), the flow velocity of the same size as that of the front portion appeared at the rear of the structure, and the uniform flow was prominent at the downstream end. However, in the case of b = 0.0 (inactive condition), the separation of flow due to inactive condition was well seen in the rear part of the structure. This can be seen better in Figure 5 (b) showing the kerosene velocity in the vicinity of the structure. The location and size of the maximum flow rate showed a big difference according to the length of activity. The simulation results of the uniform depth are shown in FIG. 5 (c). For b = ∞, there was no drop and rise in the water level at the front and rear of the structure, and only parallel levels were observed. On the other hand, in case of b = 0.0, the separation of the flow around the piers due to inactive condition is more pronounced than b = ∞, and the bow wave which rises at the front of the structure and the drop of the water level at the side of the structure And rise was well observed. On the other hand, the water drop was well behind the bridge. FIG. 5 (d) shows the streamline distribution near the structure. In the case of b = ∞, the flow velocity of the inertia force in the rear side of the pier was remarkable, but in the case of b = 0.0 It was formed and the wake phenomenon was prominent.

6 and 7 compare the results of time averaged flow rates when the partial activity condition b = 4.0 mm is applied and the inactivity and full activity condition are applied. FIG. 6 shows longitudinal kerosene velocity and flow separation occurred at b = 0.0 and 4.0 mm due to the velocity constraint condition assigned along the structure perimeter. On the other hand, in case of b = ∞, separation does not occur at the boundary layer, so there is no decrease in flow rate at the back of the structure. In the case of b = 4.0 mm, the longitudinal flow slope was larger than in the inactive condition. For b = ∞, the maximum flow rate was about 50% greater than for the other two cases. Figure 7 shows the transverse kerosene velocity and when b = 4.0 mm, the transverse velocity was reversed at a position about 4D away from the center of the structure. On the contrary, for b = ∞, lateral flow velocity is symmetric about the center of the structure.

8 shows the change in the longitudinal flow velocity component with time at three points on the back surface of the structure (D, 0), (2D, 0) and (3D, 0). In the case of Fig. 8 (a) showing the longitudinal flow rate distribution, three prominent features appeared. At the point (D, 0) indicated by the dashed line and the solid line, the reverse flow appeared over all time. At the point (2D, 0) represented by the solid circle and the empty circle, the forward and reverse flows appeared alternately. At the point (3D, 0), represented by a solid triangle and an empty triangle, there was an increase and decrease in flow velocity, but a downstream flow was observed. On the other hand, the amplitude and period of amplitude were different according to the change of the active length of b = 0.0 and 4.0 mm. On the other hand, in the case of the transverse flow rate distribution (Fig. 8 (b)), the flow rate distribution symmetrical on the y-axis was prominent by the formation of symmetrical vortices by vortex shedding.

The change pattern with time of eddy at the back of the structure is shown in FIG. 9. In this figure, the characteristics similar to the fluctuations of the flow velocity were shown. FIG. 10 contains snapshots of vortices at two specific times (tu _∞ /D=138.6, 142.0). It can be seen that the vortices alternately develop in the upper and lower parts downstream of the structure, and the phase difference and the amplitude difference occur when comparing the eddy distribution by the inactive condition indicated by the solid line and the partial activity condition indicated by the dotted line.

The longitudinal flow velocity distribution at the interface of the structure is shown in FIG. 11. In the case of full activity conditions, longitudinal maximum and minimum flow rates were found at the shoulder and back of the structure, and transverse maximum and minimum flow rates were at 45 ° and 315 °, respectively. However, under partial activity conditions, a completely different flow velocity distribution occurred due to the separation of the shear layer. In the case of b = 2.0 mm and 4.0 mm, the maximum flow rates corresponded to 10% and 20% of the upstream flow velocity, and the location of the maximum flow rate also moved 20˚ and 12˚ toward the front of the structure compared to the full activity conditions. The depth distribution at the interface of the structure is shown in FIG. 12. Since the flow of fluid is blocked by the structure, bow-wave occurs in the front of the structure, and the water level rises and then descends along the side, and the water level is the lowest at the shoulder where θ = 90 °. After approaching the rear, the water level rose again. Although the difference in water level by inactive condition and partial activity condition was not large, in the case of full activity condition, the water depth was larger than the downstream depth at the rear of the structure, resulting in physically unsuitable water level distribution. As a result of the above numerical simulation, when the full activity conditions generally applied in the existing commercial models for domestic and foreign water flow analysis are given, the direction and magnitude of flow velocity, the rise and fall of the water level, the distribution of shear force, the drag and lift time in the vicinity of the structure Because of the inability to correctly interpret the change pattern, the flow behavior in the natural river is different from the current flow. Therefore, it can be interpreted more precisely if the partial activity conditions that control the flow of the fluid at the solid boundary are given.

While specific preferred embodiments of the present invention have been illustrated and described above, the present invention is not limited to the above-described embodiments, and a person skilled in the art to which the present invention pertains has the technical gist of the present invention. Various changes can be made without departing.

Claims (2)

(a) The central processing unit uses a program in the main memory containing the following equations, that is,

Wow

Where I, II, and III are elements containing boundary nodes C, and dA is the area of this element,

Wow

Are the shape functions at boundary node C, respectively.

Calculating and storing a tangent (-n _y , n _x ) and a normal vector (n _x , n _y ) at an interface in a natural coordinate system satisfying the partial differential in x and y directions of;
(b) inputting, by the input device, the hydrostatic pressure initial condition to which the zero flow rate and the constant depth are given to all nodes including the boundary nodes;
(c) identifying a node of a solid boundary surface in the topographic information file and storing the boundary node and the length of action (b) in the main memory by the input device;
(d) The central processing unit uses the program in the main memory including the input data and the following equations using the tangent and normal vectors, the hydrostatic initial conditions and the active length as input data. , In other words,

Wow

(Where b is the active length, n _x and n _y are the x- and y-direction components of the normal unit vector at the interface, respectively, u ₁ and u ₂ are the longitudinal and horizontal flow rates respectively). Calculating and storing the flow rates u _s1 and u _s2 at the boundary node by the edge node, and
(e) Using the initial hydrostatic pressure condition and boundary condition (upstream flow velocity, downstream depth, flow velocity at boundary node), the central processing unit inputs the input data (initial hydrostatic pressure condition and boundary condition) and The finite element method is applied to the equations so that the following equations, i.e.

,

Wow

(Where, h is the water depth, u ₁ and u ₂ are respectively the vertical and horizontal directions depth mean velocity, g is the distance, ν _T of the acceleration of gravity, n is the number of roughness indicating the roughness degree of the bed and the wall, to the charge image H is from the reference line is Computing and storing longitudinal flow velocity (excluding boundary node) and water depth (including boundary node) at any time and location satisfying the eddy viscosity, and solid boundary surface in 2D shallow water numerical modeling. How to assign partial activity conditions to.
The method of claim 1,
If the amount of change Δu ₁ , Δu ₂ , Δh of the result calculated in step (e) is larger than the allowable range of 10 ⁻⁵ , the partial activity condition is calculated by reflecting the calculated flow field (vertical flow velocity and depth). In order to reflect the boundary condition, the steps of (d) and (e) are repeated to obtain a converged flow field (u ₁ , u ₂ , h) until the process becomes smaller than the allowable range. A method for imparting partial activity conditions to a solid boundary surface in a two-dimensional shallow water numerical modeling, characterized in that it is included as.

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