Sep 2026· Communications in Computational Physics· Vol 41, pp. 536-580· 0 citations· 38 references
Abstract
In recent decades, diffuse interface methods have become popular for the simulation of multi-material flows. They consider regions where the materials may be artificially mixed and interfaces are then considered as diffuse zones. In this document, a cell-centered indirect arbitrary Lagrangian-Eulerian diffuse interface strategy is presented for solving 3D multi-material equations. The use of a compressive limiter enables to prevent excessive numerical diffusion during the remapping step. It also allows the same treatment for pure and mixed cells, the same framework for dispersed or separated phases, robust multi-material simulations and easy multiphysics extensions. To address the discrete total energy conservation issue, the total kinetic energy is remapped to correct the material internal energies. It is proved that the correction terms are positive thus enforcing thermodynamics consistency. Last but not least, stiff multi-material test cases, involving fluids with highly contrasted equations of states are carried out, demonstrating the robustness of the overall numerical strategy.
We study the discretisation of a uniaxial (rank-one) reduction of
the Oldroyd--B model for dilute polymer solutions, in which the
conformation tensor is represented as $\sig=\vec b\otimes\vec
b$. Building on structural analogies with magnetohydrodynamics
(MHD), we formulate a finite element framework compat...
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