An oscillation-free flow solver based on flux reconstruction

AGUERRE, HORACIO J.; PAIRETTI, CESAR I.; VENIER, CESAR M.; MÁRQUEZ DAMIÁN, SANTIAGO; NORBERTO M. NIGRO

JOURNAL OF COMPUTATIONAL PHYSICS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2018 vol. 365 p. 135 - 148

0021-9991

In this paper, a segregated algorithm is proposed to suppress high-frequency oscillationsin the velocity field for incompressible flows. In this context, a new velocity formulabased on a reconstruction of face fluxes is defined eliminating high-frequency errors. Inanalogy to the Rhie?Chow interpolation, this approach is equivalent to including a flux-based pressure gradient with a velocity diffusion in the momentum equation. In order toguarantee second-order accuracy of the numerical solver, a set of conditions are definedfor the reconstruction operator. To arrive at the final formulation, an outlook over thestate of the art regarding velocity reconstruction procedures is presented comparing themthrough an error analysis. A new operator is then obtained by means of a flux differenceminimization satisfying the required spatial accuracy. The accuracy of the new algorithmis analyzed by performing mesh convergence studies for unsteady Navier?Stokes problemswith analytical solutions. The stabilization properties of the solver are then tested in aproblem where spurious numerical oscillations arise for the velocity field. The results showa remarkable performance of the proposed technique eliminating high-frequency errorswithout losing accuracy.