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A moving grid method applied to one‐dimensional non‐stationary flame propagation
Author(s) -
Mack A.,
Weber H. J.,
Roth P.
Publication year - 1991
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.1650130705
Subject(s) - method of lines , partial differential equation , mathematics , solver , multigrid method , numerical partial differential equations , grid , ordinary differential equation , method of characteristics , differential equation , mathematical analysis , mathematical optimization , differential algebraic equation , geometry
The paper presents applications of a moving grid method to the combined problem of ignition and premixed flame propagation in a closed vessel. This method belongs to the general class of adaptive grid techniques for the numerical integration of evolutionary partial differential equations and is based on the method of lines with variable node position. In the present case the motion of the grid and the solution of the partial differential equations are strongly coupled by an implicit formulation. The problem is reduced to an initial value problem for a stiff differential‐algebraic system. The continuously moving grid is determined by the equidistribution of a positive function which depends on the solution of the partial differential equations. A differential‐algebraic system solver is used for the time integration of the initial value problem. The numerical results of the test problems demonstrate the computational efficiency and the capability of the method to resolve the main features of the solution.