High-Order Positivity-Preserving Kinetic Schemes for the Compressible Euler Equations

Abstract

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