Finite volume methods for solving hyperbolic problems on euclidean manifolds without radially symmetric initial condition

Abstract

Many interesting physical systems are successfully modeled with time-dependant conservation laws on smooth manifolds, M. Examples of such systems include hydrodynamic flows in non-trivial geometry, important in aerodynamic modeling. Though in many applications the manifold is simply Euclidean space;M = ∇3, the curvilinear basis on which computes is non-orthogonal and quite complicated. The finite volume methods have very important property of ensuring that basic quantities such as mass, momentum and energy are conserved at a discrete level. Conservation is satisfied over each control volume, over a group of control volumes and over the entire solutiondomain. The finite volume methods are used to solve conservation laws on Euclidean manifold.