Central Differencing Based Numerical Schemes for Hyperbolic Conservation Laws with Relaxation Terms

Many applications involve hyperbolic systems of conservation laws with source terms. The numerical solution of such systems may be challenging, especially when the source terms are stiff. Uniform accuracy with respect to the stiffness parameter is a highly desirable property but it is, in general, very difficult to achieve using underresolved discretizations. For such problems we develop different second order uniformly accurate high-resolution nonoscillatory central schemes. The schemes retain the simplicity of central schemes for hyperbolic conservation laws and avoid the use of Riemann solvers. In particular, we show that these schemes possess a discrete analogue of the continuous asymptotic limit and are able to capture the correct behavior even if the initial layer and the small relaxation time are not numerically resolved.