ON POSITIVITY PRESERVING FINITE-VOLUME SCHEMES FOR EULER EQUATIONS

We consider the positivity preserving property of first and higher ord er finite volume schemes for one and two dimensional Euler equations o f gas dynamics. A general framework is established which shows the pos itivity of density and pressure whenever the underlying one dimensiona l first order building block based on an exact or approximate Riemann solver and the reconstruction are both positivity preserving. Appropri ate Limitation to achieve a high order positivity preserving reconstru ction is described.