A projection hybrid high order finite volume/finite element method for incompressible turbulent flows

TL;DR

This paper extends a hybrid finite volume/finite element method for incompressible turbulent flows to include species transport and turbulence modeling, introducing high-order schemes and analyzing their accuracy and stability.

Contribution

It develops high-order accurate schemes for transport diffusion, extends the ADER method to 3D, and integrates turbulence modeling into the hybrid FV/FE framework.

Findings

The new schemes achieve high-order accuracy in 3D simulations.

The method effectively models turbulent flows with species transport.

Numerical tests confirm the stability and accuracy of the proposed approach.

Abstract

In this paper the projection hybrid FV/FE method presented in Busto et al. 2014 is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the $k-\varepsilon$ model. Regarding the transport diffusion stage new schemes of high order of accuracy are developed. The CVC Kolgan-type scheme and ADER methodology are extended to 3D. The latter is modified in order to profit from the dual mesh employed by the projection algorithm and the derivatives involved in the diffusion term are discretized using a Galerkin approach. The accuracy and stability analysis of the new method are carried out for the advection-diffusion-reaction equation. Within the projection stage the pressure correction is computed by a piecewise linear finite element method. Numerical results are presented, aimed at verifying the formal order of accuracy of the scheme and to assess the performance of the method on several realistic test problems.