Gene

Statistics

Epistemology

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Geodesy

Mathematical analysis

Philosophy

Classification of discontinuities

Numerical stability

Finite difference

Chemistry

Benchmark (surveying)

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Simple (philosophy)

Applied mathematics

Mathematics

Conservation law

Order of accuracy

Computer science

Computational science

Numerical analysis

Finite volume method

Biochemistry

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Robustness (evolution)

Stencil

Spurious relationship

Journal of Computational Physics

In this paper, a new type of high-order finite difference and finite volume multi-resolution weighted essentially non-oscillatory (WENO) schemes is presented for solving hyperbolic conservation laws. We only use the information defined on a hierarchy of nested central spatial stencils and do not introduce any equivalent multi-resolution representation. These new WENO schemes use the same large stencils as the classical WENO schemes in [25], [45], could obtain the optimal order of accuracy in smooth regions, and could simultaneously suppress spurious oscillations near discontinuities. The linear weights of such WENO schemes can be any positive numbers on the condition that their sum equals one. This is the first time that a series of unequal-sized hierarchical central spatial stencils are used in designing high-order finite difference and finite volume WENO schemes. These new WENO schemes are simple to construct and can be easily implemented to arbitrary high order of accuracy and in higher dimensions. Benchmark examples are given to demonstrate the robustness and good performance of these new WENO schemes.

A new type of multi-resolution WENO schemes with increasingly higher order of accuracy