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Domain mappings for the numerical solution of partial differential equations
Author(s) -
Oberkampf William L.
Publication year - 1976
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620100116
Subject(s) - mathematics , numerical partial differential equations , partial differential equation , separable partial differential equation , distributed parameter system , partial derivative , domain (mathematical analysis) , first order partial differential equation , stochastic partial differential equation , mathematical analysis , differential equation , variable (mathematics) , method of characteristics , differential algebraic equation , ordinary differential equation
Independent variable transformations of partial differential equations are examined with regard to their use in numerical solutions. Systems of first order and second order partial differential equations in conservative and nonconservative form are considered. These general equations are transformed using generalized mapping functions and important computational features of the transformed equations are discussed. Examples of mappings which regularize domains are given involving various types of partial differential equations. These mappings are of particular importance in finite difference approximations because of the ease with which a mesh can be adapted to regions formed by co‐ordinate lines.