TY - JOUR

T1 - The effect of nonlinear transformations on the computation of weak solutions

AU - Zwas, Gideon

AU - Roseman, Joseph

N1 - Funding Information:
Unfortunately, unlike the classical situation, this uniqueness depends on the form of the given system of partial differential equations. In other words, a nonlinear transformation of the original dependent variables leads to a different * On leave from Tel Aviv University, Israel. t Supported by NSF Grant GP-27960.

PY - 1973/2

Y1 - 1973/2

N2 - For a nonlinear hyperbolic system, computational methods yield different weak solutions for different forms of the system. An explanation is given of the numerical mechanism by which a scheme selects a particular weak solution and why this mechanism depends not only on the scheme but also on the form of the equations. For the Lax-Friedrichs and Lax-Wendroff schemes, it is shown how a correction term can be added to a transformed system so as to preserve the weak solution. This analysis is illustrated by numerical shock-like solutions of the equations of shallow fluid flow over a ridge.

AB - For a nonlinear hyperbolic system, computational methods yield different weak solutions for different forms of the system. An explanation is given of the numerical mechanism by which a scheme selects a particular weak solution and why this mechanism depends not only on the scheme but also on the form of the equations. For the Lax-Friedrichs and Lax-Wendroff schemes, it is shown how a correction term can be added to a transformed system so as to preserve the weak solution. This analysis is illustrated by numerical shock-like solutions of the equations of shallow fluid flow over a ridge.

UR - http://www.scopus.com/inward/record.url?scp=2542610310&partnerID=8YFLogxK

U2 - 10.1016/S0021-9991(73)80009-9

DO - 10.1016/S0021-9991(73)80009-9

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AN - SCOPUS:2542610310

SN - 0021-9991

VL - 12

SP - 179

EP - 186

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 2

ER -