A Pseudospectral Method with Edge Detection-Free Postprocessing for Two-Dimensional Hyperbolic Heat Transfer

Abstract

Under the governing equations of hyperbolic heat transfer, thermal disturbances travel with a finite speed of propagation and are visible as sharp discontinuities in the solution profiles. As a result of the well-known Gibbs phenomenon, the numerical solution of hyperbolic heat transfer problems by high-order numerical methods such as pseudospectral methods feature nonphysical numerical oscillations. For pseudospectral methods, postprocessing methods have been developed to lessen or even eliminate the effects of the Gibbs phenomenon. The most powerful postprocessing methods require that the exact location of the discontinuities be known. Because of the reflection and interaction of thermal waves, the solutions of multidimensional hyperbolic heat transfer problems often have very complex features that make accurately locating discontinuities difficult or even impossible. The application of an edge detection-free postprocessing method that is effective for this type of problem is discussed.