Application of a minimal compatible element to incompressible and nearly incompressible continuum mechanics

An implicit staggered hybrid finite volume/finite element solver for the incompressible Navier-Stokes equations

We present a novel fully implicit hybrid finite volume/finite element method for incompressible flows. Following previous works on semi-implicit hybrid FV/FE schemes, the incompressible Navier-Stokes equations are split into a pressure and a transport-diffusion subsystem. The first of them can be seen as a Poisson type problem and is thus solved efficiently using classical continuous Lagrange finite elements. On the other hand, finite volume methods are employed to solve the convective subsystem, in combination with Crouzeix-Raviart finite elements for the discretization of the viscous stress …

On thermodynamically compatible finite volume schemes for continuum mechanics

In this paper we present a new family of semi-discrete and fully-discrete finite volume schemes for overdetermined, hyperbolic and thermodynamically compatible PDE systems. In the following we will denote these methods as HTC schemes. In particular, we consider the Euler equations of compressible gasdynamics, as well as the more complex Godunov-Peshkov-Romenski (GPR) model of continuum mechanics, which, at the aid of suitable relaxation source terms, is able to describe nonlinear elasto-plastic solids at large deformations as well as viscous fluids as two special cases of a more general first …

连续介质力学 GPR 模型的半隐式混合有限体积/有限元方法

Semi-implicit hybrid finite volume/finite element method for the GPR model of continuum mechanics

本文提出一种求解不可压缩和弱可压缩介质的半隐式混合有限体积/有限元数值方法，基于 Godunov-Peshkov-Romenski (GPR) 模型推导新公式，通过系统分裂策略实现高效求解，并在多种基准测试中验证了二阶精度与鲁棒性。

用于二维可压缩非线性弹性力学的二阶协调应变混合有限元

Second-Order Compatible-Strain Mixed Finite Elements for 2D Compressible Nonlinear Elasticity

本文为位移梯度和应力张量制定了具有显式形函数的二阶协调应变混合有限元，通过向量微积分与Piola变换构建高效形函数，验证了其在有限应变近不可压缩固体模拟中的数值稳定性。

面向单元中心近不可压缩弹性的核感知双网格预条件子

A Kernel-Aware Two-Grid Preconditioner for Cell-Centered Nearly Incompressible Elasticity

针对近不可压缩弹性混合离散的约化系统，提出结合位移与离散旋度粗空间的双网格预条件子，使条件数独立于Lamé比，实验验证其有效性。

一种用于近不可压缩多网络流体弹性力学的混合有限元方法

A mixed finite element method for nearly incompressible multiple-network poroelasticity

本文提出并分析了一种新的混合有限元格式，用于求解准静态多网络流体弹性力学（MPET）方程，解决了近不可压缩情况下的数值离散问题，并通过数值实验验证了其鲁棒性。

非结构化多边形网格上连续介质力学的一种几何与热力学相容有限体积格式

A geometrically and thermodynamically compatible finite volume scheme for continuum mechanics on unstructured polygonal meshes

提出非结构化多边形网格上的新型有限体积格式，通过嵌入两个正交守恒修正同时满足GCL与热力学第二定律，并在SHTC模型和测试中验证其结构保持性质。

A robust and scalable unfitted adaptive finite element framework for nonlinear solid mechanics

In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics problems posed on complex geometries, as an alternative to standard body-fitted formulations, unstructured mesh generation and graph partitioning strategies. We pay special attention to those aspects requiring a specialized treatment in the extension of the unfitted h-adaptive aggregated finite element method on parallel tree-based adaptive meshes, recently …

一种用于连续介质力学的保结构且热力学相容的单元中心拉格朗日有限体积格式

A structure-preserving and thermodynamically compatible cell-centered Lagrangian finite volume scheme for continuum mechanics

本文针对拉格朗日形式的GPR连续介质力学模型，提出一种在移动非结构网格上同时满足离散总能量守恒、离散熵不等式、密度与畸变场行列式相容以及无旋性质精确保持的半离散单元中心有限体积格式。

High order ADER schemes for continuum mechanics

In this paper we first review the development of high order ADER finite volume and ADER discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in 1999 by Toro et al. We show the modern variant of ADER based on a space-time predictor-corrector formulation in the context of ADER discontinuous Galerkin schemes with a posteriori subcell finite volume limiter on fixed and moving grids, as well as on space-time adaptive Cartesian AMR meshes. We then present and discuss the unified symmetric hyperbolic and thermodynamically compatible (SHTC) formulation of continuum mecha…

一种用于稳定边缘解析不可压缩无粘流中不连续压力投影算子的后处理技术

A post-processing technique for stabilizing the discontinuous pressure projection operator in marginally-resolved incompressible inviscid flow

本文提出一种后处理方法，用于稳定低分辨率不可压缩无粘流的不连续元方法，通过改善压力投影速度场的光滑性和减少发散，提升稳定性与守恒性。

一种准确的有限元方法用于粘性流体等温不可压缩流动的数值求解

An accurate finite element method for the numerical solution of isothermal and incompressible flow of viscous fluid

本文提出了一种无需稳定化或分裂方案的通用方法，用于求解粘性流体流动问题，通过平衡方程直接求解，提高了计算的准确性和鲁棒性，适用于多物理场应用。