CN102147932A - Method for simulating smog driven by movable Euler grid-based model - Google Patents

Abstract

The invention discloses a method for simulating smog driven by a movable Euler grid-based model, which comprises the following three steps of: discretizing a calculable space by using an Euler grid and computing the motion state of the smog through physical calculation; allowing the Euler grid and the smog in the Euler grid to synchronously move with the model and allowing the smog in the grid to change in the motion state under the action of the driving force of the model; and visualizing the smog by an improved feeling method to achieve the effect that the tail smog moves along the model. According to the method, the motion effect of the tail smog driven by the model can be achieved, and the method has the advantage of real time.

Description

A kind of smoke simulation method of the model-driven based on removable Euler's grid

Technical field

The present invention relates to a kind of smoke simulation method of the model-driven based on removable Euler's grid.

Background technology

In field of Computer Graphics, people are attempting using a computer always and are reproducing natural scene on every side, and wherein the smog animation is an important branch; The face shaping irregular of fluid phenomenons such as smog, there are not smooth surface and shape to change along with the time, this makes describes powerlessly to it with classical geometry, as going modeling with straight line, circular arc and SPL etc., then its fidelity is understood poor.

Traditionally, generally use methods such as particIe system or process texture to realize the simulation of fluid phenomenon.Along with the raising of hardware computing power, obtain gradually paying attention to based on the analogy method of physics.This method is based on the physics law of smog movement, use Navier Stokes equation (the Navier-Stokes Equation in the fluid mechanics, hereinafter to be referred as the N-S equation) as theoretical model, therefore truer more reasonable, the while can better be handled the interaction mode of smog and external environment.

Therefore, become research topic the hottest in the field of Computer Graphics gradually, received increasing concern, had important scientific research to be worth based on the fluid simulation of physics.In addition, the simulation of fluid such as smog also has important practical significance and using value.This and numerous application demand are closely bound up, and the sense of reality to the smog animation in video display special efficacy, battlefield emulation, recreation, animation, advertisement requires all very urgent.

Complicated calculations when being to find the solution partial differential equation based on the problem of the smoke simulation method maximum of physics causes it to be difficult to guarantee real-time.Up to 1996, Foster and Metaxes just used the motion of having simulated the smoke and gas streams based on the method for physics at three dimensions, and two people adopt explicit method when finding the solution the N-S equation, but there is the problem of less stable in this method, and had only the single order precision.In the smog sense of reality still is that performance aspect the real-time does not comply with one's wishes, and is difficult to reach the effect that needs in the application.

For solving the stability problem that explicit method brings, Stam has introduced half Lagrange (Semi-Lagrangian) method of a kind of unconditional stability and has handled when finding the solution this system of equations, this method can guarantee when adopting bigger time step that the phenomenon of " Blow up " can not appear in smog.Like this, owing to can use bigger simulated time step-length, reduced the frequency of smog physical computing, thereby arithmetic speed and stability have been improved, target to real-time calculating has strided forward major step, from then on after, the research of adopting the N-S equation to simulate three dimensional fluid begins more and more general.

But this method can be brought a large amount of numerical dissipations or energy loss, thereby causes some typical small scale whirlpools to disappear too soon, the feature of some details aspects of can erasing.Researcher afterwards is general on the basis of this method, and the method that searching can remedy the numerical dissipation that it brings improves the sense of reality of simulation.When Fedkiw etc. carry out visual Simulation to cigarette, adopt the method that increases whirlpool that the energy loss that numerical dissipation causes is replenished the field of refluxing, obtained the effect of dense smoke turbulent flow.

In computer graphical, people expect the effect and the method for solving of fast and stable more really more, and this just need seek the equilibrium point of an optimum between authenticity and speed, so that obtain satisfied drafting effect when guaranteeing real-time.Fluid such as smog and external environment mutual also is based on an important problem in the fluid simulation of physics always in addition, and comprising the effect of extraneous barrier to smog, external influence power is to the control of smog movement form etc.This reciprocation can be by being embodied the parameter adjustment in the N-S equation, and then drive smog and flow according to set mode.

Because the physical computing amount is bigger, the smoke simulation scope can be subjected to the restriction of Euler's sizing grid or population in the existing method.Just need to enlarge the grid scope or increase population if obtain the smog scene of big resolution, can make the calculating quantitative change big, thereby have influence on the real-time of smoke simulation.Often need simulated automotive tail gas in application scenarioss such as recreation, battlefield emulation, tail gas is followed automobile and is synchronized with the movement in this class problem, expansion to a certain extent the smog scope, increased calculated amount.Pfaff etc. and Cohen etc. are respectively in 2009 with realized the effect of vehicle exhaust in 2010 with method separately, wherein Pfaff focus on use the method for synthetic disturbance to obtain better boundary effect, Cohen then has been used in combination the boundary that particle method is handled Euler's boundary, but the analog rate of the tail gas that these two kinds of methods obtain is all relatively slow.

Summary of the invention

The technical problem to be solved in the present invention is: overcome the deficiencies in the prior art, a kind of smog tail gas simulate effect based on physics law is provided, and when guaranteeing the smoke simulation sense of reality, by simplifying the speed that physical computing improves real time modelling.

The technical solution used in the present invention is: the smoke simulation method based on the model-driven of removable Euler's grid is characterized in that having comprised following three steps:

(1) sets up the physical model of smog movement, but use Euler's grid discretization computer memory, finding the solution of physical model is decomposed into horizontal transport item, diffusion term, external force item and projection item, and, draw Euler's grid internal aerosol in difference physical state constantly by finding the solution these four in real time based on the method for GPU.

(2) will be limited to Euler's grid inside based on the smog of physics by the boundary condition that smog is set, and Euler's grid and inner smog thereof are synchronized with the movement with model, model-driven power acts on the physical model of smog by the external force item and changes the motion state of smog;

(3) use improved object plotting method, the physical quantity of visable representation smog movement state, thus obtain smog tail gas effect with model sport.

In the foundation of described smog movement physical model, employed theoretical model N-S equation:

$\frac{\mathrm{du}}{\mathrm{dt}}=-\▿p/\mathrm{\ρ}+\mathrm{\υ}{\▿}^{2}u+f---\left(1\right)$

Wherein u is the movement velocity of smoke units, and p is the pressure between smoke units, and ρ represents smoke density, and υ represents the coefficient of viscosity of smog, and f is the whole external force that aerosol is subjected to.Calculate for simplifying, hypothesis smog is homogeneity among the present invention, and promptly υ is a constant, and claims that formula (1) is the equation of momentum of smog.Simultaneously because real-life smoke density changes little, hypothesis smog is incompressible among the present invention, be that the global density of smog in motion process do not change, and because smog movement meets law of conservation of mass, so incompressible smog volume does not change, thereby can obtain the incompressible equation of following smog in motion process:

$\▿\·u=0---\left(2\right)$

So far can obtain complete physical model, suppose that promptly smog is the fluid of incompressible homogeneity, coincidence formula (1) and formula (2), this paper is collectively referred to as the N-S system of equations of smog with two formula, and the method for back will be launched around finding the solution this system of equations.

Finding the solution of N-S system of equations is the problem of finding the solution partial differential equation on the mathematics in essence.The present invention uses the computing method of finite difference, at first the zoning discretize, come the variate-value of approximate continuity distribution then with the variable on one group of discrete point, derivative can come approximate representation with the algebraic expression of discrete value, the problem of finding the solution of partial differential equations has just changed into the problem of finding the solution of Algebraic Equation set like this, thereby has simplified calculated amount.

In the described spatial discretization method, the present invention adopts regular cube Euler grid to come the whole computer memory of discretize, and this method can be used bigger time step, and the easier parallel characteristics of utilizing GPU is quickened the calculating of smoke condition simultaneously.Stored smog in each cube grid in computable physical quantitys such as the speed of this position, pressure, density, what pay close attention in the computation process is the variation of physical quantity in each cube grid; But this cubical computer memory has limited the bounds of smog simultaneously.

By the N-S system of equations is carried out a series of mathematical derivation, can draw following computing formula:

$\frac{\∂u}{\∂t}=P(-u\·\▿u+v{\▿}^{2}u+f)---\left(3\right)$

Wherein P is a self-defining projection operation, Pw=Pu=u is arranged, wherein

The front has been introduced this paper use and has been found the solution partial differential equation based on the finite difference method of spatial discretization, as long as therefore obtain the velocity field u that the right-hand component of formula (3) can be tried to achieve smog.

In the described system of equations numerical computation method, the present invention is decomposed into advection item, diffusion term, external force item and projection item with finding the solution of formula (3) right half part and finds the solution respectively, and in the solution procedure of advection item, use implicit expression integration method and MACCORMACK method to improve the speed and the sense of reality of smoke simulation, in the solution procedure of diffusion term and projection item, then use the real-time that guarantees simulation based on the Jacobi iteration of interpolation method.

In the described model driven method based on removable Euler's grid, the smog physical state find the solution the mesh space inside that the space is limited in certain limit, in case the motion of smog exceeds computable mesh space, smog will no longer move according to physics law.Therefore, need be that the smog field sets a boundary condition, the motion of smog is limited to computable mesh space inside, boundary condition is as follows:

u＝0

(4)

$\∂p/\∂n=0$

Shortcoming based on the smoke simulation method of Euler's grid is that smoke simulation is subjected to the constraint of grid scope.When simulated automotive tail gas, be synchronized with the movement and expanded the smog scope because tail gas is followed automobile, increased calculated amount.Can find by observing, in fact the smog scope itself that occurs as tail gas does not enlarge, just move with model owing to smog, cause the position of Euler's grid of smoke simulation that respective change takes place, but and then need wider computer memory could realize simulation motion tail gas.In order not increase calculated amount, among the present invention smog is limited to Euler's grid inside, and Euler's grid and inner smog thereof are synchronized with the movement with model, thereby under the prerequisite that does not increase the smog scope, simulated the motion morphology of vehicle exhaust.

For simulated exhaust gas is subjected to the effect of the proal reverse momentum of vehicle, need increase an external force backward to the smog of simulated exhaust gas, travel forward thereby obtain vehicle, and the rendering effect that tail gas is oppositely discharged backward.Tail gas smog also is subjected to the acting force backward of a vehicle traction except being subjected to normal physical action like this, and this acting force puts on the physical motion of smog by the external force item.

It should be noted that the influence that is subjected to Euler's mesh motion, the speed of moving smoke units also needs to take place corresponding variation in the grid.Influenced by relative motion, certain variation has taken place in the smoke units speed in Euler's grid of motion, and establishing its former speed is u _Local, mesh motion speed is v ₀, u here _LocalAnd v ₀Be vector and direction is opposite, then to the absolute velocity u of removable Euler's grid smoke units _WolrdHave:

u _wolrd＝u _local+v ₀ (5)

In removable Euler's grid method, the boundary condition of smog field need change, and this moment, needing the absolute velocity of revision boundary smoke units was zero, i.e. u in order to guarantee that smog does not exceed the border of computing grid _Wolrd=0, boundary condition is modified to like this:

u _local＝-v ₀ (6)

In the described improved object plotting method,, use the Raycast method to realize the visual of smog physical state three-D grain then by access point and the direction that pre-computation methods has been preserved throw light at the RayData three-D grain.When the volume data for the treatment of drafting is sampled, improved the speed of volume drawing among the present invention by judgement sampling stop condition, phenomenons such as band or the distortion of smog edge appear when avoiding playing up simultaneously, in per half small cubes grid, use the shake texture to determine sampling step length, simultaneously smog is carried out rim detection, take high-resolution sampling plan at boundary, so both can obtain rendering effect preferably, can not cause the calculated amount of drawing excessive again.

In a word, compared with prior art, the present invention has designed a kind of movably Euler grid, and has simulated the effect that the smog tail gas of model-driven is synchronized with the movement with model on this basis.This method needn't enlarge the grid scope, does not therefore increase the physical computing amount of smoke simulation, can obtain the good real-time performance effect under the prerequisite that guarantees the smog tail gas sense of reality.

Description of drawings

Fig. 1 is a smoke simulation process flow diagram used in the present invention;

Fig. 2 is used for Euler's grid of discretize computer memory for the present invention;

Fig. 3 is a physical computing step used in the present invention;

The light sampling system condition synoptic diagram of Fig. 4 object plotting method used in the present invention;

Fig. 5 removable Euler's grid synoptic diagram used in the present invention;

The smog tail gas design sketch that Fig. 6 draws for the present invention;

The smog tail gas movement effects figure that Fig. 7 obtains for the present invention.

Embodiment

In order to realize smoke simulation method based on physics law, shown in the process flow diagram among Fig. 1, at first need to set up a suitable physical model, then model is carried out numerical solution, draw the physical state (being physical quantitys such as speed, density) of each frame smog, play up with improved object plotting method again, as time passes, draw continuous smog movement state in conjunction with the constraint condition of smog.

The present invention supposes that smog is incompressible homogeneity fluid, and to draw the physical model of N-S system of equations as smoke simulation thus.

Real-life gas can compress, but promptly uses piston that gas is compressed, and the variation of its density is also also little.Therefore this paper method supposes that at first smog is incompressible, and promptly the global density of smog in motion process do not change.Simultaneously because smog movement meets law of conservation of mass, so incompressible smog volume does not change in motion process.

To definite regional Ω in the smog, its boundary representation is for can pass through boundary integral

Calculate the rate of change of smog volume in the Ω zone.For incompressible smog,, can obtain formula (7) because volume change is zero:

${\∫\∫}_{\∂\mathrm{\Ω}}u\·n=0---\left(7\right)$

Use high formula difficult to understand again, the area branch can be converted into the volume branch:

${\∫\∫\∫}_{\mathrm{\Ω}}\▿\·u={\∫\∫}_{\∂\mathrm{\Ω}}u\·n=0---\left(8\right)$

Because the smog incompressibility in any zone is all set up, therefore above-mentioned integration and integral domain are irrelevant, can release the incompressible equation shown in the formula (2).

Can draw the equation of momentum shown in the formula (1) by force analysis then to smoke units, and because hypothesis smog is homogeneity, so the viscosity coefficient υ of smog is a constant.

Can draw the N-S system of equations of forming by formula (1) and formula (2) thus, and suppose that smog is a kind of incompressible fluid of homogeneity, be i.e. the physical model of smog movement.

Finding the solution of N-S system of equations is the problem of finding the solution partial differential equation on the mathematics in essence, but because the computing method operand in fluid mechanics field is excessive, be difficult to realize real-time smoke simulation, therefore be necessary in graphics, the method for solving of N-S system of equations to be made some simplification.

The present invention uses the computing method of finite difference to find the solution partial differential equation, come the variate-value of approximate continuity distribution with the variable on one group of discrete point, derivative can come approximate representation with the algebraic expression of discrete value, partial differential equation has just become one group of algebraic equation like this, and the problem of finding the solution of partial differential equations has just changed into the problem of finding the solution of Algebraic Equation set.It is at first discrete in computable space with system of equations to use finite difference method to need.

Non-individual body discretization method commonly used comprises Lagrangian method and Euler's method.These two kinds of methods respectively have characteristics, Lagrangian method is as a kind of motion of paying close attention to particle itself based on the method for particle, more pay attention to the details of fluid, and the processing thinking of Euler method is simple relatively, and can use bigger time step, therefore better aspect real-time, more be easily extended to parallel computation simultaneously.When the present invention is not the fluid that enriches especially in this details of processing smog, for the real-time that guarantees to use, selected the less Euler method of calculation cost, this discretization method based on grid is easier to utilize the parallel characteristics of GPU simultaneously, quickens the calculating of smoke condition.As shown in Figure 2, for further improving arithmetic speed, the cube grid of alternation rule of the present invention comes the whole computer memory of discretize, stored smog in each little cube grid in computable physical quantitys such as the speed of this position, pressure, density, what pay close attention in the computation process is the variation of physical quantity in each cube grid; But this cubical computer memory has then limited the bounds of smog.

Can draw formula (3) by the N-S system of equations by a series of mathematical derivations then, and will be decomposed into advection item, diffusion term, pressure term, projection item and calculate respectively, as shown in Figure 3.

In the finding the solution of advection item, the present invention has at first used the implicit expression method for solving, and this method can realize on GPU easily, and is unconditional stability, allows to use time step arbitrarily, thereby has improved the speed of physical computing.But this implicit expression computing method have also been introduced some numerical value dissipation of energies, make smog can lose some details.In order to remedy the loss of details, the present invention passes through to introduce the MACCORMACK method in the fluid mechanics again,, use the horizontal transport item method for solving of twice implicit expression to come calculated level transmission item, improved the precision of smoke simulation.

In the solution procedure of diffusion term and projection item, all relate to iterative operation, used Jacobi iteration among the present invention, improved computing velocity, and convergence is preferably arranged based on interpolation method.

And in the solution procedure of external force item, the present invention has considered gravity, buoyancy and has been used to remedy the whirlpool constraining force of smog loss of detail that these applied external force have influence on smog movement by the external force item.

Provided among the present invention false code below based on the smog computing method of physics:

Can be by aforesaid computing method in the hope of the physical quantitys such as speed of smog at difference moment diverse location place, following the present invention stores these physical quantitys in a series of three-D grains into, uses that improved object plotting method is visual has stored the motion state that these three-D grains can draw smog.

The method of general at present use volume drawing realizes the visual of 3 d data field, because therefore data are fit to use ray cast (RayCasting) method to realize the visual of volume data by on the discrete net point that is evenly distributed on the three-dimensional cubic volume mesh among the present invention.

For to body throw light to be drawn, the amount that need know comprises: light enters body (being access point) wherefrom, the direction of light and the number of times of sampling (can the validity and the render speed of rendering result be exerted an influence) etc.For the method that has adopted a kind of precomputation among two amounts the present invention of front, deposit the value of needs in a three-D grain that is called RayData Texture, wherein access point leaves the rgb passage of texture in, and the ray degree of depth under this projection access point and the direction then deposits in a passage.

Can obtain the access point and the light degree of depth of whole throw lights by searching RayData Texture when drawing smog, and projecting direction can be made difference by current view point and access point and can obtain.Can on whole volume data, sample thus, and draw out the three-dimensional data that obtains before by suitable blend of colors method according to the projecting direction of storage before.

The computing formula of blend of colors is as shown in Equation (9):

FinalColor.rgb+＝SampleColor.rgb×SampleColor.a×(1-FinalColor.a)

(9)

FinalColor.a+＝SampleColor.a×(1-FinalColor.a)

Here in order to improve drafting efficient, also need to use some optimization methods.Problematic drawing result such as bar zoning or the distortion of smog edge appear when playing up in the present invention, in per half small cubes grid, use the shake texture to determine sampling step length, simultaneously smog is carried out rim detection, take high-resolution sampling plan at boundary, so both can obtain rendering effect preferably, and can not cause the calculated amount of drawing excessive again.After introducing barrier, the situation of two kinds of influence samplings may occur, as shown in Figure 4, irregular solid is represented the barrier in the smog field among the figure.

First kind of situation is shown in light a among Fig. 4, there is the part aerosol to be blocked by barrier, here viewpoint is to the minimum value of obstacle distance, that is: on light length that the condition that can being provided with samples stops to be preserved among the RayData Texture for the light degree of depth surpasses and the employing direction

rayLength＞＝min(length _raydata，length _obstacle) (10)

Another kind of situation, shown in light b among Fig. 4, aerosol is blocked by barrier fully, at this moment also need the comparison viewpoint on aerosol front surface and the sample direction viewpoint to the distance of blocking barrier, if viewpoint arrives the distance of barrier to aerosol front surface distance greater than it, then aerosol is sheltered from fully by barrier as can be known, needn't consider ray cast herein when sampling again.The condition that stops ray cast being as shown in Equation (11):

length _smoke＞＝length _obstacle (11)

It is the distance that viewpoint arrives barrier on the sample direction more than or equal to viewpoint to the distance of smog.Can draw out the motion state of smog so fast really.

Though the smoke simulation based on Euler viewpoint can real time modelling go out sense of reality smog, its shortcoming is that smoke simulation is subjected to the constraint of grid scope.Just need to enlarge the grid scope if obtain the smog scene of big resolution, thereby make that the calculating quantitative change is big.

Often need simulated automotive tail gas problem in application scenarioss such as recreation, battlefield emulation, tail gas is followed automobile and is synchronized with the movement in this class problem, expansion to a certain extent the smog scope, increased calculated amount.But can find by observing, in fact the smog scope itself that occurs as tail gas does not enlarge, just move with model owing to smog, cause the position of Euler's grid of smoke simulation that respective change takes place, but and then need wider computer memory could realize simulation motion tail gas.In order not increase calculated amount, this paper research and realized a kind of based on the smoke simulation method of Euler's grid movably, thereby under the prerequisite that does not increase the smog scope, realized the smog movement of model-driven, simulated the motion morphology of vehicle exhaust.

For simulated exhaust gas is subjected to the effect of the proal reverse momentum of vehicle, need increase an external force backward to the smog of simulated exhaust gas, travel forward thereby obtain vehicle, and the rendering effect that tail gas is oppositely discharged backward.Tail gas smog also is subjected to the acting force backward of a vehicle traction except being subjected to normal physical action like this.For simplifying computing, the present invention supposes that this acting force is a constant constant, and it is put on the external force item.It should be noted that the influence that is subjected to Euler's mesh motion, the speed of moving smoke units also needs to take place corresponding variation in the grid.As shown in Figure 5, be subjected to the influence of relative motion, certain variation has taken place in the smoke units speed in moving Euler's grid, and establishing its former speed is u _Local, mesh motion speed is v ₀, the absolute velocity u of smoke units then _WolrdBe u _LocalAnd v ₀Sum.

Based on Euler's grid movably, the boundary condition of smog also needs corresponding variation takes place, and is modified to u _Local=-v ₀By this movably Euler grid method, under the prerequisite that does not enlarge the computing grid scope, effectively simulated automotive tail gas is with the effect of motor racing.And when automobile stops, owing to inertia effect tail gas can be subjected to a forward action power preshoot phenomenon takes place, produce mutual with the automobile that stops.

As shown in Figure 6, showed that smog is followed vehicle together with the proal synoptic diagram of identical speed as tail gas in the scene, wherein smog is limited cube grid inside in the drawings, and along with vehicle travels forward together.

Fig. 7 then is the smog tail gas movement effects figure that the present invention obtains.

Table 1 is the simulation frame per second comparing result of the present invention and Pfaff2009 method and Cohen2010 method.Can see that Euler's grid resolution that the present invention uses is lower, therefore not enough to the simulation of smog details, in order to remedy the deficiency of this respect, the present invention has used the Jacobi iteration 60 times, and has still obtained higher frame per second.In the concrete real-time application, by reducing the Jacobi number of iterations, the present invention can obtain the frame per second of per second about 26～90 frame/seconds, and when 90 frames/second pretty good drafting effect is arranged still, therefore the present invention is fit to the application in the real time environment more, and can access tail gas effect preferably.

Table 1

The content that is not described in detail in the instructions of the present invention belongs to this area professional and technical personnel's known prior art.

Claims (2)

1. based on the smoke simulation method of the model-driven of removable Euler's grid, it is characterized in that comprising following three steps:

(1) sets up the physical model of smog movement, but utilize Euler's grid discretization computer memory, finding the solution of physical model is decomposed into horizontal transport item, diffusion term, external force item and projection item, and, draw Euler's grid internal aerosol in difference physical state constantly by finding the solution above-mentioned four in real time based on the method for GPU;

(2) by the boundary condition that smog is set the smog that obtains is limited to Euler's grid inside, and Euler's grid and inner smog thereof are synchronized with the movement with physical model, the driving force that uses a model acts on the physical model of smog and changes the motion state of smog;

(3) use improved object plotting method, the visual smog movement state that obtains, thus obtain smog tail gas effect with model sport.

2. method according to claim 1 is characterized in that: described step (2) is specially:

(1) by the boundary condition of smog movement is set, make that the smog movement speed of boundary is zero, thus the range of movement of restriction smog;

(2) Euler's grid and model projection are arrived same three dimensions, guarantee that the two is synchronized with the movement, on the basis that is synchronized with the movement, revise the boundary condition of smog simultaneously;

(3), thereby change the motion state of smog by the model-driven masterpiece being used for the external force item of smog physical model, and the smog tail gas effect of using smog movement effects under external force to come analogy model to drive.

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