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Positivity--preserving numerical scheme for hyperbolic systems with δ− shock solutions and its convergence analysis

Ganesh Vaidya, GD Gowda
Published in
2020
Abstract

Godunov type numerical schemes for the class of hyperbolic systems, admitting non-classical shocks are proposed. It is shown that the numerical approximations converge to the solution and preserve the physical properties of the system such as positive density and bounded velocity. The scheme has been extended to positivity preserving and velocity bound preserving second-order accurate scheme by using appropriate slope limiters. The numerical results are compared with the existing the literature and the scheme is shown to capture the solution efficiently. The paper presents a hyperbolic system, for which an entropy satisfying scheme is constructed through an appropriate decoupling of the system into two scalar conservation laws with discontinuous flux.