Abstract
We present a second-order scheme for the numerical solution of hyperbolic systems which treats space and time in a unified manner. The flow variables and their slopes are the basic unknowns in the scheme. The scheme utilizes the advantages of the space–time conservation element and solution element (CE/SE) method of Chang [1995] as well as central schemes of Nessyahu and Tadmor [1990]. However, unlike the CE/SE method the present scheme is Jacobian-free and hence like the central schemes can also be applied to any hyperbolic system. In Chang's method, a finite difference approach is being used for the slope calculation in case of non-linear hyperbolic equations. We propose to propagate the slopes by a scheme even in the case of non-linear systems. By introducing a suitable limiter for the slopes of flow variables, we can apply the same scheme to linear and non-linear problems with discontinuities. The scheme is simple, efficient and has a good resolution especially at contact discontinuities. We derive the scheme for one- and two-space dimensions. In two-space dimensions we use structured triangular meshes. The second-order accuracy of the scheme has been verified by numerical experiments. Several numerical tests presented in this article validate the accuracy and robustness of the present scheme.
Sign-in/Register to access full text options 
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.
