Active flux scheme for time-dependent, viscous, compressible flows

Sugar-Gabor, O

Abstract

The Active Flux scheme is a Finite Volume scheme with additional degrees of freedom on the cell
boundaries. These additional nodes allow for third-order accuracy to be achieved, though extensions to
higher orders are also possible. Unlike Godunov-type Finite Volume schemes, Active Flux makes use of a
continuous reconstruction across the cell faces and does not require a Riemann solver. The variable values
at the additional degrees of freedom on the cell faces are evolved independently from the cell-average
values, using (non-conservative) compact-stencil schemes most suited to the mathematical and physical
properties of the equations being solved. Overall conservation is enforced via the cell-average values which
are updated in a step following the evolution of the additional degrees of freedom. The fundamentals of the
Active Flux scheme are presented using a simple application on the Burgers equation. An evolution operator
for both linear and nonlinear hyperbolic conservation systems is presented and then extended to include
source terms. Example 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 an operator splitting approach. These allow for the Active Flux evolution operators to
be applied to the numerical computation of viscous, compressible flows.

Citation

Sugar-Gabor, O. (2022, October). Active flux scheme for time-dependent, viscous, compressible flows. Presented at International Conference of Aerospace Sciences AEROSPATIAL 2022, INCAS, Bucharest, Romania

• Presentation Conference Type: Keynote
• Conference Name: International Conference of Aerospace Sciences AEROSPATIAL 2022
• Conference Location: INCAS, Bucharest, Romania
• Start Date: Oct 13, 2022
• End Date: Oct 14, 2022
• Publication Date: Oct 13, 2022
• Deposit Date: Nov 25, 2022
• Publisher: National Institute for Aerospace Research “Elie Carafoli”
• Publisher URL: https://aerospatial-2022.incas.ro/
• Additional Information: Event Type : Conference