论文信息 - A penalization method applied to the wave equation

A penalization method applied to the wave equation

Abstract In this Note we investigate the mathematical properties of the volume penalization method applied to the one-dimensional wave equation. Generally speaking, the penalization method allows one to handle complex geometries by simply adding a term to the equation to impose the boundary conditions. We study the convergence of the method with regards to the penalization parameter and we present error and stability analyses for the wave equation. Numerical simulations using a finite difference scheme illustrate the results. To cite this article: A. Paccou et al., C. R. Mecanique 333 (2005).

Jacques Liandrat | Kai Schneider | Guillaume Chiavassa | Aymeric Paccou

[1] Roland Glowinski,et al. Wavelet and Finite Element Solutions for the Neumann Problem Using Fictitious Domains , 1996 .

[2] J. Ferziger,et al. A ghost-cell immersed boundary method for flow in complex geometry , 2002 .

[3] Rosa Donat,et al. Point Value Multiscale Algorithms for 2D Compressible Flows , 2001, SIAM J. Sci. Comput..

[4] Nicholas K.-R. Kevlahan,et al. Computation of turbulent flow past an array of cylinders using a spectral method with Brinkman penalization , 2001 .

[5] Philippe Angot,et al. Analysis of singular perturbations on the Brinkman problem for fictitious domain models of viscous flows , 1999 .

[6] Khodor Khadra,et al. Fictitious domain approach for numerical modelling of Navier–Stokes equations , 2000 .

[7] Kai Schneider,et al. Adaptive Wavelet Simulation of a Flow around an Impulsively Started Cylinder Using Penalisation , 2002 .

[8] C. Peskin. The immersed boundary method , 2002, Acta Numerica.

[9] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[10] Philippe Angot,et al. A penalization method to take into account obstacles in incompressible viscous flows , 1999, Numerische Mathematik.

[11] C. Peskin. Flow patterns around heart valves: A numerical method , 1972 .