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Application of the method of lines to unsteady compressible Euler equations
Author(s) -
Šolín Pavel,
Segeth Karel
Publication year - 2003
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.450
Subject(s) - mathematics , backward euler method , discretization , euler method , runge–kutta methods , ode , euler equations , linearization , smoothness , mathematical analysis , euler's formula , semi implicit euler method , method of lines , lipschitz continuity , numerical analysis , ordinary differential equation , differential equation , nonlinear system , differential algebraic equation , physics , quantum mechanics
Abstract In the sense of method of lines, numerical solution of the unsteady compressible Euler equations in 1D, 2D and 3D is split into three steps: First, space discretization is performed by the first‐order finite volume method using several approximate Riemann solvers. Second, smoothness and Lipschitz continuity of RHS of the arising system of ordinary dimensional equations (ODEs) is analysed and its solvability is discussed. Finally, the system of ODEs is integrated in time by means of implicit and explicit higher‐order adaptive schemes offered by ODE packages ODEPACK and DDASPK, by a backward Euler scheme based on the linearization of the RHS and by higher‐order explicit Runge–Kutta methods. Time integrators are compared from several points of view, their applicability to various types of problems is discussed, and 1D, 2D and 3D numerical examples are presented. Copyright © 2003 John Wiley & Sons, Ltd.