Semi-implicit Roe-type Fluxes for Low-mach Number Flows

Two semi-implicit methods based on the splitting of the Euler equations ux into uid and acoustic parts applied to low Mach number ows are presented. The rst method is based on the splitting of slow and fast eigenvalues of the jacobian matrix of the uxes and a semi-implicit scheme is constructed by introducing only the fast eigenvalues in the implicit matrices. The second method is based on the splitting of the Euler ux by separating the terms in velocity and the terms in pressure ; this system is solved by a fractional step method. A semi-implicit scheme is obtained by using a linearised implicit scheme for the acoustic step only. These two methods are applied to the convection of a density pulse for Mach numbers equal to 0.1 and 0.01. Accuracy and eeciency of the diierent schemes are compared.