Abstract
In this paper, we develop a so-called Entropy-TVD scheme for the non-linear scalar conservation laws. The scheme simultaneously simulates the solution and one of its entropy, and in doing so the numerical dissipation is reduced by carefully computing the entropy decrease. We prove that the scheme is feasible and TVD and satisfies the entropy condition. We also prove that the local truncation error of the scheme is of first-order. However, numerical tests show that the scheme has a second-order convergence rate, an order higher than its truncation error, in computing smooth solution, and in many cases is better than a second-order ENO scheme in resolving shocks and corners of rarefaction waves.
Sign-in/Register to access full text options 
Free) 
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 call
