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A note on discontinuous numerical solutions of the kinematic wave motion
Author(s) -
Lewis R. W.,
Morgan K.,
Pugh E. D. L.,
Smith T. J.
Publication year - 1984
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620200313
Subject(s) - classification of discontinuities , kinematics , kinematic wave , mathematics , finite element method , basis (linear algebra) , mathematical analysis , shock wave , motion (physics) , element (criminal law) , domain (mathematical analysis) , equations of motion , classical mechanics , geometry , physics , mechanics , engineering , structural engineering , ecology , political science , surface runoff , law , biology
This note discusses the numerical solution of the kinematic wave equation under those conditions when the solution contains a discontinuous shock. A finite element solution is described in which shocks are represented by discrete nodal discontinuities. The implementation of the method follows conventional finite element practice over the shockless regions of the solution domain which are coupled by frontal constraints. The basis of the method and examples of its application to the solution of the kinematic wave equation in one and two dimensions are presented.