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Discrete particle simulations are widely used to study large-scale particulate flows in complex geometries where particle-particle and particle-fluid interactions require an adequate representation but the computational cost has to be kept…

Computational Engineering, Finance, and Science · Computer Science 2017-11-02 Christoph Rettinger , Ulrich Rüde

In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of…

Numerical Analysis · Mathematics 2025-10-23 Ruben Caraballo , Chansophea Wathanak In , Alberto F. Martín , Ricardo Ruiz-Baier

We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the…

comp-gas · Physics 2008-02-03 Balu Nadiga , Dale Pullin

A stable finite element scheme that avoids pressure oscillations for a three-field Biot's model in poroelasticity is considered. The involved variables are the displacements, fluid flux (Darcy velocity), and the pore pressure, and they are…

Numerical Analysis · Mathematics 2016-05-03 Xiaozhe Hu , Carmen Rodrigo , Francisco J. Gaspar , Ludmil T. Zikatanov

We consider Riemann surfaces obtained from nodal curves with infinite cylinders in the place of nodal and marked points, and study the space of finite energy vortices defined on these surfaces. To compactify the space of vortices, we need…

Symplectic Geometry · Mathematics 2015-07-23 Sushmita Venugopalan

We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…

Numerical Analysis · Mathematics 2023-01-30 Michel Duprez , Vanessa Lleras , Alexei Lozinski

We consider a space-time finite element method on fully unstructured simplicial meshes for optimal sparse control of semilinear parabolic equations. The objective is a combination of a standard quadratic tracking-type functional including a…

Numerical Analysis · Mathematics 2020-04-01 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

For Laplace operator in one space dimension, we propose to formulate the heuristic finite volume method with the help of mixed Petrov-Galerkin finite elements. Weighting functions for gradient discretization are parameterized by some…

Numerical Analysis · Mathematics 2014-01-07 François Dubois

This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…

Numerical Analysis · Mathematics 2024-10-30 Xiaojuan Wang , Jihong Xiao , Xiaoping Xie , Shiquan Zhang

This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of…

Numerical Analysis · Mathematics 2014-01-29 Douglas N. Arnold , Richard S. Falk , Ragnar Winther

This article investigates a space-time differential model related to the degradation of stone artifacts caused by exposure to air and atmospheric agents, which specifically lead to the accumulation of salt crystals in the material. A…

Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed…

Computational Physics · Physics 2014-11-04 A. B. Stamm , B. A. Shadwick

In this paper we construct a family of steady symmetric vortex patches for the incompressible Euler equations in an open disk. The result is obtained by studying a variational problem in which the kinetic energy of the fluid is maximized…

Analysis of PDEs · Mathematics 2019-09-04 Daomin Cao , Guodong Wang , Bijun Zuo

We introduce a pressure robust Finite Element Method for the linearized Magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presence of high fluid and magnetic Reynolds numbers. The proposed…

Numerical Analysis · Mathematics 2024-01-03 L. Beirão da Veiga , F. Dassi , G. Vacca

An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on…

Numerical Analysis · Mathematics 2020-02-19 Longfei Li

We present a simple modification of the direct-forcing immersed boundary method (IBM) proposed by Uhlmann [J. Comput. Phys, 2005] in order to enable it to be applied to particulate flows with solid-to-fluid density ratios around unity. The…

Fluid Dynamics · Physics 2023-06-21 Manuel Garcia-Villalba , Blanca Fuentes , Jan Dusek , Manuel Moriche , Markus Uhlmann

We develop two unfitted finite element methods for the Stokes equations using $H^{\text{div}}$-conforming finite elements. Both methods achieve optimal convergence for velocity, ensure pointwise divergence-free velocity fields, and produce…

Numerical Analysis · Mathematics 2024-09-04 Thomas Frachon , Erik Nilsson , Sara Zahedi

We introduce a new family of high order accurate semi-implicit schemes for the solution of non-linear hyperbolic partial differential equations on unstructured polygonal meshes. The time discretization is based on a splitting between…

Numerical Analysis · Mathematics 2023-09-11 Walter Boscheri , Andrea Chiozzi , Michele Giuliano Carlino , Giulia Bertaglia

In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…

Numerical Analysis · Mathematics 2025-09-05 Sudheer Mishra , E Natarajan

Unconditionally stable finite element methods for Darcy flow are derived by adding least-squares residual forms of the governing equations to the classical mixed formulations. The proposed methods are free of mesh dependent stabilization…

Numerical Analysis · Mathematics 2025-05-27 Maicon R. Correa , Abimael F. D. Loula