Analysis of selected standard implicit schemes with arbitrary mesh movement

Abstract

Two methods that can he used with moving meshes are developed for the solution of the I-D Euler equations. The methods are derived by applying the Beam and Warming implicit procedure to the strong conservation law form (SCLF) and chain rule conservation law form (CRCLF) of the governing equations. The modified equations for the methods are developed and analyzed. The analysis shows that the standard Beam and Warming procedures are only first-order accurate in time when used with a moving mesh, and that the following are desirable qualities for a solution adaptive mesh; smooth mesh movement, high resolution around solution gradients, and mesh movement at the same speed as the propagation velocity of the local solution features. Numerical results are obtained for a 1-D shock tube model problem using meshes that test the desirable mesh qualities. The results indicate that; 1 .) the methods are only first-order accurate in time and exhibit large solution dissiption, 2.) solution accuracy can be improved by using meshes that have the desirable qualities, 3.) the SCLF and CRCLF methods are qualitatively identical for meshes without abrupt variations in mesh point speeds.