In this paper, we consider the issue of convergence toward entropy solutions for high order finite volume weighted essentially non-oscillatory (WENO) scheme and discontinuous Galerkin (DG) finite element method approximating scalar nonconvex conservation laws. Although such high order nonlinearly stable schemes can usually converge to entropy solutions of convex conservation laws, convergence m...

In our talk, we propose an adaptive mesh-refining strategy for the cell-centered FVM based on some a posteriori error control for the quantity ‖∇T (u − Iuh)‖L2 . Here, uh ∈ P (T ) denotes the FVM approximation of u and I is a certain interpolation operator. As model example serves the Laplace equation with mixed boundary conditions, where our contributions extend a result of [NIC05]. Moreover, ...

We develop a discretization scheme for the coupling of the finite volume method and the boundary element method in two dimensions, which describes, for example, the transport of a concentration in a fluid. The discrete system maintains naturally local conservation. In a bounded interior domain we approximate a diffusion convection reaction problem either by the finite volume element method or b...

Improved Finite-Volume Method for Radiative Hydrodynamics Alan Wray* Corresponding author: [email protected] * NASA Ames Research Center, USA Abstract: Fully coupled simulations of hydrodynamics and radiative transfer are essential to a number of fields ranging from astrophysics to engineering applications. Of particular interest in this work are hypersonic atmospheric entries and associate...

A parallel solvers package of three solvers with a unified user interface is developed for solving a range of sparse symmetric complex linear systems arising from disc~tization of partial differential equations based on unstructu~d meshs using finite element, finite difference and finite volume analysis. Once the data interface is set up, the package constructs the sparse symmetric complex matr...

The thin plate is a key structure in various musical instruments, including many percussion instruments and the soundboard of the piano, and also is the mechanism underlying electromechanical plate reverberation. As such, it is a suitable candidate for physical modelling approaches to audio effects and sound synthesis, such as finite difference methods—though great attention must be paid to the...

A finite volume scheme is discussed for discretizing diffusion operators. Both cell-center unknowns and cell-vertex unknowns are used originally in the construction of the finite volume scheme. Then cell-vertex unknowns are eliminated by expressing them locally as linear combinations of cell-center unknowns, which is derived by the following process. First we construct a special control-volume ...