From: Friedemann Kemm Subject: Re: rieman solver Date: Wed, 31 Jan 2001 11:15:04 +0100 Newsgroups: sci.math.num-analysis Summary: Numerically solving Riemann problems (conservation laws) On 31 Jan 2001, see.signature wrote: > lastly I came across the term rieman solver in cfd literature. Can > someone explain to me what a rieman solver is? The Riemann problem is the initial value problem for a conservation law in which You have constant states at the left and the right hand side and a discontinutiy in the middle. If You have a solution of this You can easily compute the flux over the place where in the beginning was the discontinuity. Now this can be used for construction of numerical schemes e.g. for Euler equations. If You discretice Your computational domain in grid cells and approximate the solution by piecewise constant (constant on the grid cells) and take an appropriate time step You have non interacting Riemann problems in the cell faces. The solutions of this Riemann problems lead You to the numerical fluxes over the cell interfaces. Now a Riemann solver is an algorithm for an exact or approximate solution of Riemann problems. For more details You may have a look at the book of E.F. Toro on this subject. Also any book that covers finite volume schemes (Kr"oner, Godlewski/Raviart,LeVeque...) will give You an introduction to Riemann solvers. Sincerely Friedemann -- ___________________________________________________________________________ | | | | Friedemann Kemm | Pfaffenwaldring 21, 70550 Stuttgart | | Institut fuer Aerodynamik | phone: +49 711/685-3454 | | und Gasdynamik (IAG) | fax : +49 711/685-3438 | | Universitaet Stuttgart | email: kemm@iag.uni-stuttgart.de | | | url : www.iag.uni-stuttgart.de/ | | | people/friedemann.kemm | ___________________________________________________________________________ ============================================================================== From: Berend van Wachem Subject: Re: rieman solver Date: Thu, 01 Feb 2001 11:28:41 +0100 Newsgroups: sci.math.num-analysis > For more details You may have a look at the book of E.F. Toro on this > subject. Also any book that covers finite volume schemes (Kr"oner, > Godlewski/Raviart,LeVeque...) will give You an introduction to Riemann > solvers. If you've never heard of the Riemann problem and/or Riemann solvers it might be advisable to start with the book "Computational Gasdynamics" by C.B. Laney Berend.