An efficient class of increasingly high-order ENO schemes with multi-resolution

Abstract

We construct an efficient class of increasingly high-order (up to 17th-order) essentially non-oscillatory schemes with multi-resolution (ENO-MR) for solving hyperbolic conservation laws. The candidate stencils for constructing ENO-MR schemes range from the first-order one-point stencil increasingly up to the designed very high-order stencil. The proposed ENO-MR schemes adopt a simple and efficient strategy that only requires the computation of the highest-order derivatives of a part of candidate stencils. Theoretical analysis and numerical computations indicate that ENO-MR schemes achieve designed high-order convergence in smooth regions which may contain high-order critical points (local extrema) and retain ENO property for strong shocks. Moreover, the performance of ENO-MR schemes does not depend on the scale of the solutions.