Flux-Based Finite Volume representations for general thermal problems

Abstract

Flux-Based Finite Volume (FV) element representations for general thermal problems are given in conjunction with a generalized trapezoidal gamma-T family of algorithms, formulated following the spirit of what we term as the Lax-Wendroff based FV formulations. The new flux-based representations introduced offer an improved physical interpretation of the problem along with computationally convenient and attractive features. The space and time discretization emanate from a conservation form of the governing equation for thermal problems, and in conjunction with the flux-based element representations give rise to a physically improved and locally conservative numerical formulations. The present representations seek to involve improved locally conservative properties, improved physical representations and computational features; these are based on a 2D, bilinear FV element and can be extended for other cases. Time discretization based on a gamma-T family of algorithms in the spirit of a Lax-Wendroff based FV formulations are employed. Numerical examples involving linear/nonlinear steady and transient situations are shown to demonstrate the applicability of the present representations for thermal analysis situations.