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 - https://www.scopus.com/pages/publications/2542610310
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 -