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SUMMARYThis paper introduces a new scheme for the numerical computation involving shock waves. The essence of the scheme is to adaptively implement a conjugate low-pass ÿlter to e ectively remove the accumulated numerical errors produced by a set of high-pass ÿlters. The advantages of using such an adaptive algorithm are its controllable accuracy, relatively low cost and easy implementation. Numerical examples in one and two space dimensions are presented to illustrate the proposed scheme.

This paper explores the potential of a newly developed conjugate filter oscillation reduction (CFOR) scheme for shock-capturing under the influence of natural high-frequency oscillations. The conjugate low-pass and high-pass filters are constructed based on the principle of the discrete singular convolution. Two Euler systems, the advection of an isentropy vortex flow and the interaction of shock-entropy wave are considered to demonstrate the utility of the CFOR scheme. Computational accuracy and order of approximation are examined and compared with the literature. Some of the best numerical results are obtained for the shock-entropy wave interaction. Numerical experiments indicate that the proposed scheme is stable, conservative and reliable for the numerical simulation of hyperbolic conservation laws.

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