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Journal of Scientific Computing

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01-04-2020

Efficient Implementation of Adaptive Order Reconstructions

Authors: M. Semplice, G. Visconti

Published in: Journal of Scientific Computing | Issue 1/2020

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Abstract

Including polynomials with small degree and stencil when designing very high order reconstructions is surely beneficial for their non oscillatory properties, but may bring loss of accuracy on smooth data unless special care is exerted. In this paper we address this issue with a new Central \(\mathsf {WENOZ}\) (\(\mathsf {CWENOZ}\)) approach, in which the reconstruction polynomial is computed from a single set of non linear weights, but the linear weights of the polynomials with very low degree (compared to the final desired accuracy) are infinitesimal with respect to the grid size. After proving general results that guide the choice of the \(\mathsf {CWENOZ}\) parameters, we study a concrete example of a reconstruction that blends polynomials of degree six, four and two, mimicking already published Adaptive Order \(\mathsf {WENO}\) reconstructions (Arbogast et al. in SIAM J Numer Anal 56(3):1818-1947, 2018),(Balsara et al. in J Comput Phys 326:780-804, 2016). The novel reconstruction yields similar accuracy and oscillations with respect to the previous ones, but saves up to 20% computational time since it does not rely on a hierarchic approach and thus does not compute multiple sets of nonlinear weights in each cell.

previous article On Efficient Numerical Solution of Linear Algebraic Systems Arising in Goal-Oriented Error Estimates

next article New Finite Difference Hermite WENO Schemes for Hamilton–Jacobi Equations

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Title: Efficient Implementation of Adaptive Order Reconstructions
Authors: M. Semplice
G. Visconti
Publication date: 01-04-2020
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2020
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01156-6

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