Abstract
Piecewise hyperbolic methods (PHMs) have been widely used for the approximation of hyperbolic conservation laws. In this paper we have studied the "power limiters" in order to analyze their suitable use in the design of PHMs. We formulate a new PHM, based on these limiters, improving the behavior of the PHM in [SIAM J. Sci. Comput., 15 (1994), pp. 892-915], at local extrema, jump discontinuities, and discontinuities in derivative. We show that this new hyperbolic reconstruction (we call it PowerPHM) is local total variation bounded and it behaves stably with a reduced numerical viscosity compared to PHM. We show numerical evidence of the above mentioned features by means of one- and two-dimensional numerical tests with the Euler equations of gas dynamics.
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