An entropic solver for ideal Lagrangian magnetohydrodynamics

In this paper; we adapt to the ideal 1D lagrangian MHD equations a class of numerical schemes of order one in time and space presented in an earlier paper and applied to the gas dynamics system. They use some properties of systems of conservation laws with zero entropy flux which describe fluid models invariant by galilean transformation and reversible for regular solutions. These numerical schemes satisfy an entropy inequality under CFL conditions. In the last section, we describe a particular scheme for the MHD equations and show with some numerical applications its robustness and accuracy. The generalization to full Eulerian multidimensional MHD will be the subject of a forthcoming paper. (C) 1999 Academic Press.