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On the numerical integration of multi‐dimensional, initial boundary value problems for the Euler equations in quasi‐linear form
Author(s) -
Valorani Mauro,
Favini Bernardo
Publication year - 1998
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199811)14:6<781::aid-num4>3.0.co;2-m
Subject(s) - mathematics , curvilinear coordinates , euler equations , boundary value problem , mathematical analysis , partial differential equation , backward euler method , euler method , geometry
A matricial formalism to solve multi‐dimensional initial boundary values problems for hyperbolic equations written in quasi‐linear based on the λ scheme approach is presented. The derivation is carried out for nonorthogonal, moving systems of curvilinear coordinates. A uniform treatment of the integration at the boundaries, when the boundary conditions can be expressed in terms of combinations of time or space derivatives of the primitive variables, is also presented. The methodology is validated against a two‐dimensional test case, the supercritical flow through the Hobson cascade n.2, and in three‐dimensional test cases such as the supersonic flow about a sphere and the flow through a plug nozzle. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 781–814, 1998