Commit 44919740 by Philippe Helluy

### up

parent 9274cfa1
 ... ... @@ -542,11 +542,11 @@ $In this section, we state some results about the numerical viscosity of the kinetic relaxation scheme in the one-dimensional case. This one-dimensional analysis will give us simple intuitions for adjusting the relaxation parameter in the 2D case. We consider the one-dimensional the relaxation parameter in the two-dimensional case. We consider the one-dimensional MHD-DC system (\ref{eq:mhd-1d}). For more simplicity, we will denote$\v F=\v F_{1}$and$x=x_{1}$. The equations then read $\partial_{t}\v w+\partial_{x}\v F(\vw)=0 \partial_{t}\v w+\partial_{x}\v F(\vw)=0.$ For the analysis, it is possible to replace the scalar relaxation ... ... @@ -596,7 +596,7 @@$ \] Finally, this analysis provides a way to numerically approximate, up to second order in time the second-order system of conservation up to second order in time, the second-order system of conservation laws \partial_{t}\vw+\partial_{x}\vF(\vw)-\partial_{x}\left(\v A(\vw)\partial_{x}\vw\right)=0.\label{eq:equiv-eq-2order} ... ... @@ -683,7 +683,7 @@ \wvec_{l}=\left(2,\frac{3}{2}\right)^{T}. \end{align} For the diffusion we use\epsilon=0.1$. For the Lattice Boltzmann scheme, we set$\lambda=40$. The results on a grid of$128^2$cells at scheme, we set$\lambda=40$. The results on a grid of$128$cells at time$T=0.1\$ are shown in Figure \ref{Fg: ViscouseShock}. The test shows that the matrix relaxation lattice Boltzmann scheme provides the correct diffusion and therefore results in the right viscous profile. ... ...
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!