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Old   January 22, 2004, 13:18
Default Steady time step
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I am trying to compute the allowable time-step at each grid point in order to satisfy the CFL condition. The problem I am solving is steady and so I can use different time-steps at each point. I realise that I need to find the max. wavespeed at each point to determine the time-step. I am using MacCormack's method and the stencil for each grid point is three points (i-1, i, i+1), so I need to consider flow conditions at all three stencil points in order to compute the allowable time-step at each grid point. However, I can't seem to be able to code this correctly. I'm using Visual C++ and have so far written:

for (i = 1; i <= no. grid points; i = i + 1)


wav = 0.0;

lambda[1] = m_old[i]/ro_old[i] - sqrt(gam*p_old[i]/ro_old[i]);

lambda[2] = m_old[i]/ro_old[i];

lambda[3] = m_old[i]/ro_old[i] + sqrt(gam*p_old[i]/ro_old[i]);

for (j = 1; j <= 3; j = j + 1)


if (fabs(lambda[j]) > wav)


wav = fabs(lambda[j]);



deltat[i] = cflno*dx/wav;


When I run my program I get a very unstable solution and I think it's due to this time-step calculation.

Any help would be greatly appreciated.

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