Work

Optimal Definition of the Nonlinear Weights in Multidimensional Central WENOZ Reconstructions

Year: 2019

Type: article

Abstract: Central $\mathsf{WENO}$ reconstruction procedures have shown very good performance in finite volume and finite difference schemes for hyperbolic conservation and balance laws in one and higher space dimensions on different types of meshes. Their most recent formulations include $\mathsf{WENOZ}$-type nonlinear weights, but in this context a thorough analysis of the global smoothness indicator $\tau$ is still lacking. In this work we first prove results on the asymptotic expansion of one- and multidimensional Jiang--Shu smoothness indicators that are useful for the rigorous design of $\mathsf{CWENOZ}$ schemes, which are in addition to those considered in this paper. Next, we introduce the optimal definition of $\tau$ for the one-dimensional $\mathsf{CWENOZ}$ schemes and for one example of two-dimensional $\mathsf{CWENOZ}$ reconstruction. Numerical experiments of one- and two-dimensional test problems show the correctness of the analysis and the good performance of the new schemes.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/18m1228232

Authors: I. Cravero, M. Semplice, G. Visconti

Institutions: University of Turin, RWTH Aachen University

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Deutsche Forschungsgemeinschaft, Gruppo Nazionale per il Calcolo Scientifico

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