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Two-grid solution of shock problems
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DOI：10.1137/S1064827595280429.png)
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The multigrid method is applied to accelerate the convergence to the steady state of hyperbolic conservation laws using two grid levels. In supersonic flow with a shock in the solution, the convergence usually slows down with the standard algorithm. By introducing a restriction, which depends on the residual, an improved effect of the coarse grid is obtained. The method is analyzed for Burgers' equation in one dimension and an explanation for the speed-up is given. The new grid transfer operators are tested on the inviscid Burgers' equation and the Euler equations in one and two space dimensions. In numerical experiments the usual transfer strategies are compared with the new one. Results for the Euler equations in two dimensions using three grids are also presented.
Keyword:
multigrid method
shocks
compressible flow
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