A New Numerical Scheme for Linear Scalar Conservation Laws
In this paper, we develop a numerical scheme with the fifth-order polynomial reconstruction satisfying two conservation laws for the linear advection equation. The scheme is the Godunov type, and has two numerical entities, numerical solution and numerical entropy. Numerical experiments show that the scheme is more robust in long-time behaviors than that of .
R. S. Chen et al., "A New Numerical Scheme for Linear Scalar Conservation Laws", Applied Mechanics and Materials, Vol. 127, pp. 65-70, 2012