Practical analytical solutions for benchmarking of 2-D and 3-D geodynamic Stokes problems with variable viscosity

I Yu Popov,S I Popov,T V Gerya,A I Popov,I S Lobanov

doi:10.5194/se-5-461-2014

Abstract

Abstract. Geodynamic modeling is often related with challenging computations involving solution of the Stokes and continuity equations under the condition of highly variable viscosity. Based on a new analytical approach we have developed particular analytical solutions for 2-D and 3-D incompressible Stokes flows with both linearly and exponentially variable viscosity. We demonstrate how these particular solutions can be converted into 2-D and 3-D test problems suitable for benchmarking numerical codes aimed at modeling various mantle convection and lithospheric dynamics problems. The Main advantage of this new generalized approach is that a large variety of benchmark solutions can be generated, including relatively complex cases with open model boundaries, non-vertical gravity and variable gradients of the viscosity and density fields, which are not parallel to the Cartesian axes. Examples of respective 2-D and 3-D MatLab codes are provided with this paper.

Highlights

Numerical modeling of geodynamic processes is recognized as a challenging computational problem which requires use of advanced computational techniques and development of powerful numerical tools (e.g., Ismail-Zadeh and Tackley, 2010, and references therein)
Benchmarking of numerical codes against analytical and numerical solutions constrained for various mechanical and thermomechanical Stokes flow problems is a common practice in computational geodynamics (e.g., Blankenbach et al, 1989; Moresi et al, 1996; van Keken et al, 2008; Gerya and Yuen, 2003, 2007; Deubelbeiss and Kaus, 2008; Duretz et al, 2011; Gerya et al, 2013; Popov, 2014; Lobanov et al, 2014; Popov and Sobolev, 2008; Tackley and King, 2003; Torrance and Turcotte, 1971; Zhong and Gurnis, 1994)
We developed new, specific analytical solutions for the 2-D and 3-D Stokes flows with both linearly and exponentially variable viscosity

Summary

Introduction

Numerical modeling of geodynamic processes is recognized as a challenging computational problem which requires use of advanced computational techniques and development of powerful numerical tools (e.g., Ismail-Zadeh and Tackley, 2010, and references therein). Benchmarking of numerical codes against analytical and numerical solutions constrained for various mechanical and thermomechanical Stokes flow problems is a common practice in computational geodynamics (e.g., Blankenbach et al, 1989; Moresi et al, 1996; van Keken et al, 2008; Gerya and Yuen, 2003, 2007; Deubelbeiss and Kaus, 2008; Duretz et al, 2011; Gerya et al, 2013; Popov, 2014; Lobanov et al, 2014; Popov and Sobolev, 2008; Tackley and King, 2003; Torrance and Turcotte, 1971; Zhong and Gurnis, 1994). Popov et al.: Benchmarking of geodynamic Stokes problems with variable viscosity

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