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 archeoptyrx August 13, 2013 13:06

Time step help in Explicit method

Hello everyone ,

I have wrote a code for solving compressible navier stokes code over a flat plate (same as given in the Anderson CFD Book) . when i tried simulating it with free stream conditions at higher altitude for example

Plate length of 1e-5 encounters slip regime above 10km altitude , which means that slip boundary conditions should be incorporated to get proper results , and the code blows up for free stream conditions above 20km (because transition regime comes into play )

Am i correct guys ? Navier stokes equation works only for continuum regime right ?

So i am using MACCORMACK Method with the time step given in book . Its because of the time step , which brings up complex numbers and its causes the program to stop .

What should i do now ?

Any suggestion will be of great help

 flotus1 August 13, 2013 13:28

While the NS equations are only valid in the continuum regime, a NS solver should still be able to produce a (wrong) solution in the rarefied regime.
If your NS code diverges for higher Knudsen numbers, there must be something wrong with the code.

 archeoptyrx August 13, 2013 13:31

Alex,

I checked the code and i find that i implemented the time step (stability criteria) wrong . This produces the complex number first which makes the solver to blow up for higher Knudsen numbers

 archeoptyrx August 13, 2013 13:35

Take a look at my time step , I implemented it wrong .

Code:

```function delt=Tstep(u,v,T,rho,mu) % K        -Fudge factor 0.5<K<0.8 % delx      - xinterval % dely      - y interval % u        - horizontal velocity at (i,j) % v        - Vertical velocity at (i,j) % a        - Speed of sound at (i,j) % mu        - Dynamic viscosity at (i,j) % Pr        - Prandtl Number % rho      - Density at (i,j) % gamma    - iscentropic constant global K Pr gamma imax jmax delx dely; % global u v T rho mu; a=Sound(T); vda=zeros(imax,jmax); deltcfl=zeros(imax,jmax); for i=1:imax     for j=1:jmax %                mu(i,j)=Dynvis(T(i,j),2);         vda(i,j)=((4*mu(i,j)*gamma*mu(i,j))/(3*rho(i,j)*Pr));     end end vdas=max(max(vda(:))); for i=1:imax     for j=1:jmax         A=abs(u(i,j))/delx;         B=abs(v(i,j))/dely;         C=a(i,j)*sqrt((1/(delx^2))+(1/(dely^2)));         D=2*vdas*((1/(delx^2))+(1/(dely^2)));         deltcfl(i,j)=(A+B+C+D)^(-1);     end end delt=real(min(min(K*deltcfl(:)))); end```

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