Fluid Dynamics Solutions Obtained from the Riemann Invariant Approach

The generalized method of characteristics is used to obtain rank-2 solutions of the classical equations of hydrodynamics in ( 3 + 1 ) dimensions describing the motion of a fluid medium in the presence of gravitational and Coriolis forces. We determine the necessary and sufficient conditions which gu...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2017-10, Vol.151 (1), p.89-119
Main Authors: Grundland, A. M., Lamothe, V.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Cauchy problems
Computational fluid dynamics
Computational Mathematics and Numerical Analysis
Coriolis force
Economic models
Fluid flow
Generalized method of moments
Gravitation
Hydrodynamics
Invariants
Mathematical analysis
Mathematics
Mathematics and Statistics
Method of characteristics
Partial Differential Equations
Probability Theory and Stochastic Processes
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Summary:The generalized method of characteristics is used to obtain rank-2 solutions of the classical equations of hydrodynamics in ( 3 + 1 ) dimensions describing the motion of a fluid medium in the presence of gravitational and Coriolis forces. We determine the necessary and sufficient conditions which guarantee the existence of solutions expressed in terms of Riemann invariants for an inhomogeneous quasilinear system of partial differential equations. The paper contains a detailed exposition of the theory of simple wave solutions and a presentation of the main tool used to study the Cauchy problem. A systematic use is made of the generalized method of characteristics in order to generate several classes of wave solutions written in terms of Riemann invariants.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-017-0104-7