Stable artificial dissipation operators for finite volume schemes on unstructured grids

Our objective is to derive stable first-, second- and fourth-order artificial dissipation operators for node based finite volume schemes. Of particular interest are general unstructured grids where the strength of the finite volume method is fully utilised.A commonly used finite volume approximation of the Laplacian will be the basis in the construction of the artificial dissipation. Both a homogeneous dissipation acting in all directions with equal strength and a modification that allows different amount of dissipation in different directions are derived. Stability and accuracy of the new operators are proved and the theoretical results are supported by numerical computations.