A NUMERICAL TREATMENT OF GEODYNAMIC VISCOUS-FLOW PROBLEMS INVOLVING THE ADVECTION OF MATERIAL INTERFACES

Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of diffe ring physical properties requires correction techniques to prevent spu rious diffusion and dispersion, We develop a particular algorithm, bas ed on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the di stribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter de signed to remove dispersion errors that result from the advection of d iscontinuities (e.g., material interfaces) by high-order, minimally di ssipative schemes. The filter introduces no additional diffusion error . Nonuniform viscosity across a material interface is allowed for by t he implementation of a compositionally weighted-inverse interface visc osity scheme. The combined method approaches the optimal accuracy of m odern shock-capture techniques with a minimal increase in computationa l time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element , or volume of two or three dimensions.