This paper presents a robust, fully Lagrangian framework based on the Particle Finite Element Method (PFEM) capable of simulating multiphase flows with an arbitrary number of immiscible phases. Interface-tracking methods can sometimes suffer from numerical diffusion or allow the underlying mesh resolution to prematurely dictate topological changes. To address these limitations, we introduce a dynamic mesh adaptation strategy that naturally preserves sharp geometric interfaces without relying on classical constrained triangulation. A node-empty disk is assigned to each segment of the discretized interface, ensuring that the edge is part of the Delaunay triangulation. Our approach decouples the interface physics from the grid size, allowing the integration of sub-grid physical models to properly govern topological changes independently of the user-defined mesh size. The capabilities and accuracy of the framework are validated against standard multiphase benchmarks, closely matching references while maintaining a remarkably low overall node count. We demonstrate the scalability and geometric versatility of the method, in particular with a challenging 16-phase Rayleigh-Taylor simulation.
Mesh generation is a critical step in the numerical simulation of computational fluid dynamics, with mesh quality directly affecting both computational efficiency and result accuracy. Traditional methods for mesh topology generation heavily rely on human expertise and heuristic algorithms, often lacking a rigorous math...
Miao-Miao Sun, Fa-Zhi Tang, Yu-Bo Li et al.· The Physics of Fluids· 0 citations
This paper introduces adaptive moving mesh methods for the numerical simulation of axisymmetric mean curvature flow, addressing both isotropic and anisotropic cases. The methods are developed within the framework of the mesh equidistribution principle, where a carefully designed tangential velocity is employed to dynam...
We develop a convergence theory for geometric multigrid with vertex-patch smoothers applied to cut finite element discretizations of the Poisson problem. The framework addresses non-inherited level forms and the mismatch between the physical and active domains. Using the discrete extension property, we prove two-level...
An adaptive multigrid method for discontinuous Galerkin formulations of elliptic problems using Brandt's full approximation scheme (FAS), designed for unstructured curvilinear meshes but maintains a tensor-product structure for fast diagonalization.
This paper introduces an adaptive mesh-based optimization framework and a practical mesh rendering technique that significantly outperforms existing mesh optimization approaches across a variety of object-centric benchmarks while being competitive with state-of-the-art NeRF/3DGS methods.
Johannes Weidenfeller, Shaofei Wang, P. Fürnstahl et al.· 0 citations
In this work, we propose an unfitted finite element scheme to approximate the solution of the heat equation on moving domains. We use the {\phi}-FEM paradigm in which the computational domain is described implicitly by a level-set function {\phi}. This function is incorporated into the variational formulation in order...
Michel Duprez, Johan Marguet, Alexei Lozinski et al.· 0 citations
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