The present paper describes new Flux Based Finite Volume element representations for general thermal problems in conjunction with a generalized trapezoidal γr - family of algorithms which are formulated following the spirit of what we term as the Lax-Wendroff based Finite Volume formulations. In comparison to the traditional control volume developments and representations adopted in the numerical solution of thermal problems, the new flux based representations introduced in this paper 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 developed in this paper seek to involve improved locally conservative properties, improved physical representations and computational features. Developments are presented here based on a two dimensional, bilinear finite volume element and can be, extended for other cases. Time discretization based on a γT -family of algorithms in the spirit of a Lax-WendrofF based Finite Volume 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.
|Original language||English (US)|
|State||Published - Jan 1 1993|
|Event||AIAA 28th Thermophysics Conference, 1993 - Orlando, United States|
Duration: Jul 6 1993 → Jul 9 1993
|Other||AIAA 28th Thermophysics Conference, 1993|
|Period||7/6/93 → 7/9/93|