HIGH-ORDER POSITIVITY-PRESERVING KINETIC SCHEMES FOR THE COMPRESSIBLEEULER EQUATIONS

We present anew class of high-order kinetic flux-splitting schemes for thr compressible Euler equations and we prove that these schemes are positivity preserving (i.e., rho and T remain greater than or equal to 0). The first-order kinetic scheme is based on the Maxwellian equilib rium function and was initially proposed by Pullin [J. Comput. Phys., 34 (1980), pp. 231-244]. Our higher-order extension can be seen as a v ariant of the corrected antidiffusive flux approach. The necessity of a limitation on the antidiffusive correction appears naturally in orde r to satisfy the constraint of positivity.