EXPLICIT TIME MARCHING METHODS FOR THE TIME-DEPENDENT EULER COMPUTATIONS

Four explicit type time marching methods, including one proposed by th e authors, are examined. The TVD conditions of this method are analyze d with the linear conservation law as the model equation. Performance of these methods when applied to the Euler equations are numerically t ested. Seven examples are tested, the main concern is the performance of the methods when discontinuities with different strengths are encou ntered. When the discontinuity is getting stronger, spurious oscillati on shows up for three existing methods, while the method proposed by t he authors always gives the results with satisfaction. The effect of t he limiter is also investigated. To put these methods in the same basi s for the comparison the same spatial discretization is used. Poe's so lver is used to evaluate the fluxes at the cell interface; spatially s econd-order accuracy is achieved by the MUSCL reconstruction. (C) 1997 Academic Press.