Constrained Reconstruction in MUSCL-Type Finite Volume Schemes

In this paper, we are concerned with the stabilization of MUSCL-type finite volume schemes in arbitrary space dimensions. We consider a number of limited reconstruction techniques which are defined in terms of inequality-constrained linear or quadratic programming problems on individual grid elements. No restrictions on the conformity of the grid or the shape of its elements are made. In the special case of Cartesian meshes, a novel QP reconstruction is shown to coincide with the widely used minmod reconstruction. The accuracy and overall efficiency of the stabilized second-order finite volume schemes are supported by numerical experiments.