Accurate determination of surface normal stress in viscous flow from a consistent boundary flux method

Abstract

Accurate determination of surface normal stresses from numerical modeling of mantle convection is crucial in determining surface topography, geoid and gravity anomalies. With the finite element method, we have developed a consistent boundary flux (CBF) method for computing the surface stress by solving the momentum equation directly. The method has a much higher accuracy for determining surface stresses than the standard pressure smoothing method, and for typical convection problems, the CBF is about one order of magnitude more accurate than pressure smoothing. The CBF can be easily applied to a variety of types of elements and to compute a range of physical quantities including heat flow on boundaries. CBF, moreover, is a post-processing operation and is computationally inexpensive.