TY - JOUR
T1 - A broad class of conservative numerical methods for dispersive wave equations
AU - Ranocha, Hendrik
AU - Mitsotakis, Dimitrios
AU - Ketcheson, David I.
N1 - KAUST Repository Item: Exported on 2021-03-25
PY - 2021/2/25
Y1 - 2021/2/25
N2 - We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta methods in time. We apply this framework to create new classes of fully-discrete conservative methods for several nonlinear dispersive wave equations: Benjamin-Bona-Mahony (BBM), Fornberg-Whitham, Camassa-Holm, Degasperis-Procesi, Holm-Hone, and the BBM-BBM system. These full discretizations conserve all linear invariants and one nonlinear invariant for each system. The spatial semidiscretizations include finite difference, spectral collocation, and both discontinuous and continuous finite element methods. The time discretization is essentially explicit, using relaxation Runge-Kutta methods. We implement some specific schemes from among the derived classes, and demonstrate their favorable properties through numerical tests.
AB - We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta methods in time. We apply this framework to create new classes of fully-discrete conservative methods for several nonlinear dispersive wave equations: Benjamin-Bona-Mahony (BBM), Fornberg-Whitham, Camassa-Holm, Degasperis-Procesi, Holm-Hone, and the BBM-BBM system. These full discretizations conserve all linear invariants and one nonlinear invariant for each system. The spatial semidiscretizations include finite difference, spectral collocation, and both discontinuous and continuous finite element methods. The time discretization is essentially explicit, using relaxation Runge-Kutta methods. We implement some specific schemes from among the derived classes, and demonstrate their favorable properties through numerical tests.
UR - http://hdl.handle.net/10754/666203
UR - http://global-sci.org/intro/article_detail/cicp/18643.html
UR - http://www.scopus.com/inward/record.url?scp=85102641162&partnerID=8YFLogxK
U2 - 10.4208/CICP.OA-2020-0119
DO - 10.4208/CICP.OA-2020-0119
M3 - Article
SN - 1991-7120
VL - 29
SP - 979
EP - 1029
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 4
ER -