Abstract
A generalization of a finite difference method for calculating numerical solutions to systems of nonlinear hyperbolic conservation laws in one spatial variable is investigated. A previously developed numerical technique called the relaxation method is modified from its initial application to solve initial value problems for systems of nonlinear hyperbolic conservation laws. The relaxation method is generalized in three ways herein to include problems involving any combination of the following factors: systems of nonlinear hyperbolic conservation laws with spatially dependent flux functions, nonzero forcing terms, and correctly posed boundary values. An initial value problem for the forced inviscid Burgers' equation is used as an example to show excellent agreement between theoretical solutions and numerical calculations. An initial boundary value problem consisting of a system of four partial differential equations based on the two‐layer shallow‐water equations is solved numerically to display a more general applicability of the method than was previously known.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
