Displaying similar documents to “Simplifying numerical solution of constrained PDE systems through involutive completion”

Simplifying numerical solution of constrained PDE systems through involutive completion

Bijan Mohammadi, Jukka Tuomela (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite general situations in a unified way. We illustrate our approach on the numerical solution of several...

Vorticity dynamics and numerical resolution of Navier-Stokes equations

Matania Ben-Artzi, Dalia Fishelov, Shlomo Trachtenberg (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical...

Numerical simulations of the humid atmosphere above a mountain

Arthur Bousquet, Mickaël D. Chekroun, Youngjoon Hong, Roger M. Temam, Joseph Tribbia (2015)

Mathematics of Climate and Weather Forecasting

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New avenues are explored for the numerical study of the two dimensional inviscid hydrostatic primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions for the system of equations. Flows above a mountain are classically treated by the so-called method of terrain following coordinate system. We avoid this discretization method which induces errors in the discretization of tangential derivatives...

On numerical solution of compressible flow in time-dependent domains

Miloslav Feistauer, Jaromír Horáček, Václav Kučera, Jaroslava Prokopová (2012)

Mathematica Bohemica

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The paper deals with numerical simulation of a compressible flow in time-dependent 2D domains with a special interest in medical applications to airflow in the human vocal tract. The mathematical model of this process is described by the compressible Navier-Stokes equations. For the treatment of the time-dependent domain, the arbitrary Lagrangian-Eulerian (ALE) method is used. The discontinuous Galerkin finite element method (DGFEM) is used for the space semidiscretization of the governing...

A penalty method for the time-dependent Stokes problem with the slip boundary condition and its finite element approximation

Guanyu Zhou, Takahito Kashiwabara, Issei Oikawa (2017)

Applications of Mathematics

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We consider the finite element method for the time-dependent Stokes problem with the slip boundary condition in a smooth domain. To avoid a variational crime of numerical computation, a penalty method is introduced, which also facilitates the numerical implementation. For the continuous problem, the convergence of the penalty method is investigated. Then we study the fully discretized finite element approximations for the penalty method with the P1/P1-stabilization or P1b/P1 element....