A method for generating boundary-orthogonal curvilinear coordinate systems using the biharmonic equation
type: Item
instance of: scholarly article
title: A method for generating boundary-orthogonal curvilinear coordinate systems using the biharmonic equation
zbMATH Open document ID: 0588.65080
DOI: 10.1016/0021-9991(85)90074-9
author: Panagiotis Demetriou Sparis
published in: Journal of Computational Physics
publication date: 1985-01-01T00:00:00Z
review text: The author presents a new method for the generation of a boundary-fitted curvilinear coordinate system which uses the biharmonic operator to generate a coordinate system with a prescribed mesh point distribution on the domain boundary. This coordinate system has coordinate lines that are normal to the domain boundary. This boundary-orthogonal coordinate system generally simplifies the application of boundary conditions expressed in the normal direction to the field boundary. The solution of the biharmonic equation is accomplished by the coupled approach that splits the problem into the solution of a Poisson and a Laplace equation. The solution of these equations is carried out in the transformed domain in a similar manner with the well-established methods of boundary-fitted coordinate system generation based on the Laplace operator, and thus retains the extremum principal. The method may also be used for the generation of meshes in segmented fields. Finally the method can be easily extended to three dimensions.
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 65N06
zbMATH DE Number: 3945306
zbMATH Keywords: Poisson equation
zbMATH Keywords: generation of a boundary-fitted curvilinear coordinate system
zbMATH Keywords: biharmonic operator
zbMATH Keywords: boundary-orthogonal coordinate system
zbMATH Keywords: Laplace equation
reviewed by: Prem Narain
MaRDI profile type: Publication
full work available at URL: 0021-9991(85)90074-9
OpenAlex ID: W2046990792
cites work: Boundary-fitted coordinate systems for numerical solution of partial differential equations. A review
cites work: TOMCAT - a code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two- dimensional bodies
cites work: Q3219062
cites work: Direct solution of the biharmonic equation using noncoupled approach
cites work: A segmentation approach to grid generation using biharmonics
cites work: A General Coupled Equation Approach for Solving the Biharmonic Boundary Value Problem
cites work: Some Difference Schemes for the Biharmonic Equation
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description: scientific article; zbMATH DE number 3945306