Progress Towards the Calculation of Time-Dependent, Viscous, Compressible Flows using Active Flux Scheme

Abstract: The Active Flux scheme is a Finite Volume scheme with additional degrees of freedom. It makes use of a continuous reconstruction and does not require a Riemann solver. An evolution operator is used for the additional degrees of freedom on the cell boundaries. This paper presents progress towards the computation of one-dimensional, viscous, compressible flows using Active Flux scheme. An evolution operator for both linear and nonlinear hyperbolic conservation systems is presented and then a novel extension is made to include source terms. Applications are made on the Euler equations and a hyperbolic formulation of the diffusion equation. Lastly, for the compressible Navier-Stokes equations, a hyperbolic formulation is presented together with a novel operator splitting approach. These allow for the Active Flux evolution operators to be applied to the numerical computation of viscous, compressible flows.