AN EXPLICIT TVD SCHEME FOR HYPERBOLIC HEAT CONDUCTION IN COMPLEX GEOMETRY

Abstract

Two-dimensional hyperbolic heat conduction problems of complex geometry are investigated numerically. A second-order total variation diminishing (TVD) scheme is introduced and its application to the hyperbolic heat conduction is developed in detail using the knowledge of characteristics. In current work primitive variables, rather than characteristic variables, are used as the dependent variables. The governing equations of two-dimensional heat conduction are transformed from the physical coordinates to the computational coordinates, so that the hyperbolic heat conduction problems of irregular geometry can be solved numerically by the present TVD scheme. Three examples with different geometry are used to verify the accuracy of the present numerical scheme. Results show the explicit TVD scheme can predict the thermal wave without oscillation.