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Bug in my Lax-Wendroff solver?

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Old   April 8, 2008, 03:05
Default Bug in my Lax-Wendroff solver?
  #1
chris
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Hi,

I am trying to implement a one step and a two-step (predictor-corrector) Lax-Wendroff solver. The one step method works perfectly, but the two-step-method produces heavy oscillations near the boundaries (dirichlet conditions) and in the vicinity of the shock when trying to solve the shock tube problem. Here some code... The timestep is chosen such that the CFL condition is satisfied.

void Solver::updateLW1(double const& dt)

{

u0=u;

for(unsigned i = 1; i < nx - 1; ++i)

u[i] = 0.5*(u0[i+1] + u0[i-1]) - 0.5*dt/dx*(flux(i+1, u0)-flux(i-1, u0)) - dt*rhs(i, u0);

}

void Solver::updateLW2(double const& dt)

{

// predictor

for(unsigned i = 1; i < nx - 1; ++i)

u0[i] = 0.5*(u[i+1] + u[i]) - 0.5*dt/dx*(flux(i+1, u)-flux(i, u)) - 0.25*dt*(rhs(i+1, u)+rhs(i, u));

// corrector

for(unsigned i = 1; i < nx - 1; ++i)

u[i] = u[i] - dt/dx*(flux(i+1, u0)-flux(i-1, u0)) + dt*rhs(i, u0);

}

Can anyone give me a hint or a link to an implementation of the predictor corrector LW-method?

Cheers, Chris
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Old   April 8, 2008, 07:31
Default Re: Bug in my Lax-Wendroff solver?
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chris
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I just solved the problem by myself. It should be flux(i, u0) instead of flux(i+1, u0) in the corrector step.
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Old   July 8, 2009, 13:32
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  #3
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Nishant Kumar
Join Date: Jun 2009
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Nishu is on a distinguished road
HI Chris,

Can you please send me the 1D code for shock tube problem at babuu.nishu@gmail.com? I need it for my research.

Thanks alot
Nishant
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