Central schemes and contact discontinuities

• Published in: ESAIM Mathematical Modelling and Numerical Analysis Vol. 34; no. 6; pp. 1259 - 1275
• Main Authors: Kurganov, Alexander, Petrova, Guergana
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 01.11.2000
• Subjects: 65M05; 65M10; Euler equations of gas dynamics; Exact sciences and technology; fully-discrete and semi-discrete central schemes; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; partial characteristic decomposition; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Discontinuity; Euler equation; Second order equation; Propagation; Gas dynamics; Differential equation; Characteristic; Conservation; Decomposition; Jacobi matrix; Contact discontinuity; Upwind scheme; Wave; Characteristic decomposition; Conservation law; Numerical computation; Discretization; Numerical solution; Hyperbolic equation; One dimensional model; Evolution; Godunov type scheme; One dimensional system; Semi discrete scheme
• ISSN: 0764-583X; 1290-3841; 1290-3841
• DOI: 10.1051/m2an:2000126

We introduce a family of new second-order Godunov-type central schemes for one-dimensional systems of conservation laws. They are a less dissipative generalization of the central-upwind schemes, proposed in [A. Kurganov et al., submitted to SIAM J. Sci. Comput.], whose construction is based on the maximal one-sided local speeds of propagation. We also present a recipe, which helps to improve the resolution of contact waves. This is achieved by using the partial characteristic decomposition, suggested by Nessyahu and Tadmor [J. Comput. Phys. 87 (1990) 408-463], which is efficiently applied in the context of the new schemes. The method is tested on the one-dimensional Euler equations, subject to different initial data, and the results are compared to the numerical solutions, computed by other second-order central schemes. The numerical experiments clearly illustrate the advantages of the proposed technique.