We consider second-order accuracy MUSCL schemes to approximate the solutions of hyperbolic system of conservation laws. In the context of the 2D unstructured grids, we propose a limitation procedure on the gradient reconstruction to enforce several stability properties. We establish that the MUSCL scheme preserves the invariant domains and satisfy a set of entropy inequalities. A conservation a...

When shock speed s times ∆t/∆x is rational, the existence of solutions of shock profile equations on bounded intervals for monotonicity preserving schemes with continuous numerical flux is proved. A sufficient condition under which the above solutions can be extended to −∞ < j < ∞, implying the existence of discrete shock profiles of numerical schemes, is provided. A class of monotonicity prese...

We present new MUSCL techniques associated with cell-centered Finite Volume method on triangular meshes. The first reconstruction consists in calculating a one vectorial slope per control volume by a minimization procedure with respect to a prescribed stability condition. The second technique we propose is based on the computation of three scalar slopes per triangle (one per edges) still respec...

A nite volume method for the numerical solution of axisymmetric inviscid swirling ows is presented. The governing equations of the ow are the axisymmetric compressible Euler equations including swirl (or tangential) velocity. A rst-order scheme is introduced. In this one, convective uxes at cell interfaces are evaluated by the Rusanov or the HLLC numerical ux and geometric source terms are disc...

A nite volume method for the numerical solution of axisymmetric inviscid swirling ows is presented. The governing equations of the ow are the axisymmetric compressible Euler equations including swirl (or tangential) velocity. A rst-order scheme is introduced. In this one, convective uxes at cell interfaces are evaluated by the Rusanov or the HLLC numerical ux and geometric source terms are disc...