In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the GLM-MHD equations: single-fluid magneto-hydrodynamics (MHD) equations with a generalized Lagrange multiplier (GLM) divergence cleaning mechanism. For continuous entropy analysis to hold and ensure Galilean invariance in technique, system requires use of non-conservat...

Techniques in the family of weighted residual methods; the orthogonal collocation, Galerkin, tau, and least-squares methods, are adopted to solve a non-linear and highly coupled pellet problem. Based on a residual measure and problem matrix condition numbers, the Galerkin and tau methods are favorable solution techniques for the pellet equations. On the other hand, the orthogonal collocation is...

—————————————————————————————————— – Abstract In this paper, we provide the collocation method for natural convection heat transfer equations embedded in porous medium which are of great importance in the design of canisters for nuclear waste disposal. This problem is a non-linear, three-point boundary value problem on semi-infinite interval. We use two orthogonal functions namely rational Gege...

In this paper, we introduce a radial basis function collocation method for computing solutions to the time-dependent radiative transfer equation. For these computations, we use finite differences to discretize the time coordinate, a discrete ordinate method to discretize the directional variable, and an expansion in radial basis functions to approximate the spatial dependence of the solution. W...