Thirty years of the finite volume method for solid mechanics

Abstract

Since early publications in the late 1980s and early 1990s, the finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of the method, which can be classified in a variety of ways, such as grid arrangement (cell-centred vs staggered vs vertex-centred), solution algorithm (implicit vs explicit), and stabilisation strategy (Rhie-Chow vs Jameson-Schmidt-Turkel vs Godunov upwinding). This article gives an overview, historical perspective, comparison and critical analysis of the different approaches where a close comparison with the de facto standard for computational solid mechanics, the finite element method, is given. The article finishes with a look towards future research directions and steps required for finite volume solid mechanics to achieve more widespread acceptance.

111 pages, 32 figures. Arch Computat Methods Eng (2021)

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• A Jacobian-free Newton-Krylov method for high-order cell-centred finite volume solid mechanics
• A cell-centred finite volume formulation of geometrically-exact Simo-Reissner beams with arbitrary initial curvatures