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Generation of Arbitrary Lagrangian–Eulerian (ALE) velocities, based on monitor functions, for the solution of compressible fluid equations
Author(s) -
Wells B. V.,
Baines M. J.,
Glaister P.
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.915
Subject(s) - conservation law , mathematics , eulerian path , discretization , euler equations , solver , mathematical analysis , compressible flow , classical mechanics , euler–lagrange equation , computational fluid dynamics , compressibility , physics , lagrangian , mathematical optimization , mechanics
A moving mesh method is outlined based on the use of monitor functions. The method is developed from a weak conservation principle. From this principle a conservation law for the mesh position is derived. Using the Helmholtz decomposition theorem, this conservation law can be converted into an elliptic equation for a mesh velocity potential. The moving mesh method is discretized using standard finite elements. Once the mesh velocities are obtained an arbitrary Lagrangian–Eulerian (ALE) ( Journal of Computational Physics 1974; 14 :227) fluid solver is used to update the solution on the adaptive mesh. Results are shown for the compressible Euler equations of gas dynamics in one and two spatial dimensions. Two monitor functions are used, the fluid density (which corresponds to a Lagrangian description), and a function which includes the density gradient. A variety of test problems are considered. Copyright © 2005 John Wiley & Sons, Ltd.