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This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…

Numerical Analysis · Mathematics 2019-04-01 Eric Chung , Yalchin Efendiev , Wing Tat Leung

This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are demonstrated for a range of benchmark…

In this paper we study a monolithic Newton-Krylov solver with exact Jacobian for the solution of incompressible FSI problems. A main focus of this work is on the use of geometric multigrid preconditioners with modified Richardson smoothers…

Computational Physics · Physics 2017-09-19 Eugenio Aulisa , Simone Bna , Giorgio Bornia

Deep learning has shown promise in improving computing efficiency while ensuring modeling accuracy in fluid-structure interaction (FSI) analysis. However, its current capabilities are limited when it comes to constructing multi-object…

Fluid Dynamics · Physics 2025-04-25 Yanfang Lyu , Yunyang Zhang , Zhiqiang Gong , Xiao Kang , Wen Yao , Yongmao Pei

We introduce a homogeneous multigrid method in the sense that it uses the same HDG discretization scheme for Poisson's equation on all levels. In particular, we construct a stable injection operator and prove optimal convergence of the…

Numerical Analysis · Mathematics 2021-08-11 Peipei Lu , Andreas Rupp , Guido Kanschat

In this contribution we present the first formulation of a heterogeneous multiscale method for an incompressible immiscible two-phase flow system with degenerate permeabilities. The method is in a general formulation which includes…

Numerical Analysis · Mathematics 2014-11-24 Patrick Henning , Mario Ohlberger , Ben Schweizer

Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…

Numerical Analysis · Mathematics 2022-09-13 Maria Vasilyeva , Alexey Sadovski , D. Palaniappan

We study a nonlinear, unsteady, moving boundary, fluid-structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is…

Analysis of PDEs · Mathematics 2015-06-05 Boris Muha , Suncica Canic

We develop a combined field formulation for the fluid structure (FS) interaction problem. The unknowns are (u;p;v), being the fluid velocity, fluid pressure and solid velocity. This combined field formulation uses Arbitrary Lagrangian…

Numerical Analysis · Mathematics 2014-01-03 Jie Liu

In this work, we propose and computationally investigate a monolithic space-time multirate scheme for coupled problems. The novelty lies in the monolithic formulation of the multirate approach as this requires a careful design of the…

Numerical Analysis · Mathematics 2024-02-27 Julian Roth , Martyna Soszyńska , Thomas Richter , Thomas Wick

We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…

Analysis of PDEs · Mathematics 2017-05-31 Clément Cancès , Claire Chainais-Hillairet , Stella Krell

A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…

Numerical Analysis · Mathematics 2020-11-25 Robert Saye

Convergence and compactness properties of approximate solutions to elliptic partial differential computed with the hybridized discontinuous Galerkin (HDG) are established. While it is known that solutions computed using the HDG scheme…

Numerical Analysis · Mathematics 2026-01-05 Jiannan Jiang , Noel J. Walkington , Yukun Yue

This paper analyzes a class of globally divergence-free (and therefore pressure-robust) hybridizable discontinuous Galerkin (HDG) finite element methods for stationary Navier-Stokes equations. The methods use the…

Numerical Analysis · Mathematics 2022-04-08 Gang Chen , Xiaoping Xie

A new hybrid mixed discontinuous Galerkin finite element (HMDGFE) method is constructed for incompressible miscible displacement problem. In this method, the hybrid mixed finite element (HMFE) procedure is considered to solve pressure and…

Numerical Analysis · Mathematics 2022-09-07 Jiansong Zhang , Yun Yu , Jiang Zhu , Rong Qin , Yue Yu , Maosheng Jiang

In this work we analyze the stability and convergence properties of a loosely-coupled scheme, called the kinematically coupled scheme, for interaction between an incompressible viscous fluid and a thin structure. We consider a benchmark…

Numerical Analysis · Mathematics 2014-06-16 Martina Bukac

In this paper we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the…

Numerical Analysis · Mathematics 2023-07-19 Jinchao Xu , Kai Yang

Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…

We propose a new discretization method for the Stokes equations. The method is an improved version of the method recently presented in [C. Lehrenfeld, J. Sch\"oberl, Comp. Meth. Appl. Mech. Eng., 361 (2016)] which is based on an…

Numerical Analysis · Mathematics 2018-03-29 Philip L. Lederer , Christoph Lehrenfeld , Joachim Schöberl

The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize…

Numerical Analysis · Mathematics 2024-05-06 Andrew Ho , Uri Shumlak