Thirty Years of the Finite Volume Method for Solid Mechanics

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.

Automated summary

The finite volume method has been proven suitable for solid mechanics analyses since the late 1980s and early 1990s. There are several variations of the method, which can be classified in different ways. This article provides an overview, historical perspective, comparison, and critical analysis of the different approaches, with a close comparison to the finite element method. It also looks towards future research directions for finite volume solid mechanics.