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We present the extension of an efficient and highly parallelisable frameworkfor incompressible fluid flow simulations to viscoplastic fluids. The system isgoverned by incompressible conservation of mass, the Cauchy momentum equationand a generalised Newtonian constitutive law. In order to simulate a wide rangeof viscoplastic fluids, we employ the Herschel-Bulkley model for yield-stressfluids with nonlinear stress-strain dependency above the yield limit. Weutilise Papanastasiou regularisation in our algorithm to deal with thesingularity in apparent viscosity. The resulting system of partial differentialequations is solved using the IAMR code (Incompressible Adaptive MeshRefinement), which uses second-order Godunov methodology for the advectiveterms and semi-implicit diffusion in the context of an approximate projectionmethod to solve on adaptively refined meshes. By augmenting the IAMR code withthe ability to simulate regularised Herschel-Bulkley fluids, we obtainefficient numerical software for time-dependent viscoplastic flow in threedimensions, which can be used to investigate systems not considered previouslydue to computational expense. We validate results from simulations using thisnew capability against previously published data for Bingham plastics andpower-law fluids in the two-dimensional lid-driven cavity. In doing so, weexpand the range of Bingham and Reynolds numbers which have been considered inthe benchmark tests. Moreover, extensions to time-dependent flow ofHerschel-Bulkley fluids and three spatial dimensions offer new insights intothe flow of viscoplastic fluids in this test case, and we provide missingbenchmark results for these extensions.

Highly parallelisable simulations of time-dependent viscoplastic fluid flow simulations with structured adaptive mesh refinement