Numerical scheme

The finite volume scheme is based on a vertex-centered approach. The solution is stored at the vertices of the primary mesh and finite volumes are constructed around each vertex, known as dual cells. The discretization is based on the ideas given in [1,2]. An advantage of this scheme is that the viscous fluxes are discretized with a very compact stencil involving only the first neighbours of each vertex. Boundary conditions are enforced in a weak manner by appropriately computing the fluxes across boundary faces. Higher order accuracy is achieved by linear reconstruction of a set of primitive variables. The gradients of the primitive variables at the vertices are computed using divergence theorem, and these gradients are exact for affine functions. Various limiters are available for computing discontinuous solutions. These include MUSCL-type schemes implemented in an edge-based manner and more multi-dimensional limiters like minmax of Barth-Jespersen and its smoothed version developed by Venkatakrishnan.

Some references

[1] http://web.stanford.edu/group/ctr/ResBriefs06/19_ham1.pdf

[2] http://www.cascadetechnologies.com/pdf/khalighi_aiaa2011.pdf