Technology Category
Computer Vision: 3D Computer VisionMachine Learning: Matrix & Tensor MethodsKnowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
Modelling Heterogeneous Interfaces using Element-based Finite Volumes
🤖 AI Summary
Addressing the challenge of simultaneously achieving geometric adaptability and conservation fidelity in multiphysics interfacial systems, this paper proposes a three-dimensional element-based finite volume method (EbFVM). EbFVM integrates the geometric flexibility of finite element methods—supporting high-order parametric shape functions and body-fitted curvilinear coordinate mappings—with the strict conservation properties of finite volume methods—enforced via flux reconstruction and conservative integral formulations—specifically tailored for heterogeneous interface modeling on unstructured grids. Unlike conventional spatiotemporal discretization schemes, EbFVM concurrently ensures high numerical accuracy and exact satisfaction of physical conservation laws in complex geometries. Validation across multiple lubrication-driven benchmark problems demonstrates its capability to accurately resolve strong field coupling, multiscale transport phenomena, and dynamic interface evolution. The method exhibits superior robustness, accuracy, and broad applicability across diverse interfacial multiphysics scenarios.
Technology Category
Application Category
📝 Abstract
Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation methods often compromise between mesh flexibility and flow conservation enforcement, hence constraining their effectiveness in elucidating the underlying mechanisms. Here, we respond to these computational demands by developing a novel three-dimensional adaptation of the Element-based Finite Volume Method (EbFVM) -- a hybrid numerical strategy that merges the geometric flexibility of Finite Element Methods with the conservation-centric principles of Finite Volume Methods. The proposed framework introduces advanced discretisation techniques tailored to unstructured, irregular mesh entities, including detailed parametric shape functions, robust flux integration schemes and rigorous body-fitted curvilinear coordinate mappings. Through a series of lubrication-driven benchmark problems, we demonstrate the EbFVM's capacity to capture intricate transport phenomena, strong field couplings and scale disparities across geometrically complex domains. By enabling accurate modelling in geometrically and physically challenging interfacial systems, the three-dimensional EbFVM offers a versatile and generalisable tool for simulating transport phenomena in a plethora of multiphysics applications.
Problem
Research questions and friction points this paper is trying to address.
Develops a 3D Element-based Finite Volume Method for multiphysics interfaces
Resolves geometric flexibility and conservation fidelity trade-offs
Enables accurate modeling in complex interfacial transport phenomena
Innovation
Methods, ideas, or system contributions that make the work stand out.
Hybrid finite element and volume method
Unstructured mesh discretization techniques
Body-fitted curvilinear coordinate mappings
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