Volumetric coupling approaches for multiphysics simulations on non‐matching meshes

Abstract

Summary In finite element analysis of volume coupled multiphysics, different meshes for the involved physical fields are often highly desirable in terms of solution accuracy and computational costs. We present a general methodology for volumetric coupling of different meshes within a monolithic solution scheme. A straightforward collocation approach is compared to a mortar‐based method for nodal information transfer. For the latter, dual shape functions based on the biorthogonality concept are used to build the projection matrices, thus further reducing the evaluation costs. We give a detailed explanation of the integration scheme and the construction of dual shape functions for general first‐order and second‐order Langrangian finite elements within the mortar method, as well as an analysis of the conservation properties of the projection operators. Moreover, possible incompatibilities due to different geometric approximations of curved boundaries are discussed. Numerical examples demonstrate the flexibility of the presented mortar approach for arbitrary finite element combinations in two and three dimensions and its applicability to different multiphysics coupling scenarios. Copyright © 2016 John Wiley & Sons, Ltd.

A monolithic, mortar‐based interface coupling and solution scheme for finite element simulations of lithium‐ion cells

“…where all integrals have been scaled by the prefactor 1 F to obtain similar orders of magnitude compared to the integrals in the preceding mass conservation equations (32) and (33).…”

“…The mortar method has already been successfully applied to various finite element simulations for interface‐coupled problems such as fluid mesh tying, structural mesh tying,() fluid‐structure interaction, and contact formulations. () Extensions of the mortar method toward volume‐coupled multiphysics problems have also been proposed . However, to the best of our knowledge, a mortar‐based interface coupling approach has not yet been developed and published for the complex Butler‐Volmer equation implemented in lithium‐ion cell models.…”

“…[26][27][28][29][30][31] Extensions of the mortar method toward volume-coupled multiphysics problems have also been proposed. 32 However, to the best of our knowledge, a mortar-based interface coupling approach has not yet been developed and published for the complex Butler-Volmer equation implemented in lithium-ion cell models. Therefore, this work attaches great value to a comprehensive, rigorous, and coherent derivation of the method, covering all essential steps from the conservation laws in strong form to the final system of linearized equations.…”

Scalable computational kernels for mortar finite element methods

“…contact mechanics including wear [30] or fluid dynamics [26], as well as a variety of surface-coupled multi-physics problems, among them fluid-structure interaction [42,47,52] or the simulation of lithium-ion cells in electrochemistry [27]. Lately, also volume-coupled problems have been addressed by mortar methods [29]. Despite their significant computational cost, the popularity of mortar methods over classical node-to-segment, Gauss-point-tosegment, and other collocation-based approaches is based on their mathematical properties such as their variational consistency and stability.…”

Scalable computational kernels for mortar finite element methods

“…contact mechanics including wear [30] or fluid dynamics [26], as well as a variety of surface-coupled multi-physics problems, among them fluidstructure interaction [42,46,51] or the simulation of lithium-ion cells in electrochemistry [27]. Lately, also volume-coupled problems have been addressed by mortar methods [29]. Despite their significant computational cost, the popularity of mortar methods over classical node-to-segment, Gauss-point-tosegment, and other collocation-based approaches is based on their mathematical properties such as their variational consistency and stability.…”