#5498. A class of high-order finite difference schemes with minimized dispersion and adaptive dissipation for solving compressible flows

August 2026publication date
Proposal available till 20-05-2025
4 total number of authors per manuscript0 $

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Journal’s subject area:
Applied Mathematics;
Numerical Analysis;
Computational Mathematics;
Modeling and Simulation;
Physics and Astronomy (all);
Physics and Astronomy (miscellaneous);
Computer Science Applications;
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Abstract:
For the compressible flows with broadband length scales, good dispersion and dissipation properties are crucial for the numerical schemes to realize high-fidelity simulations. It has been recognized that the minimization of dispersion error is an effective measure to improve the resolution of schemes. However, it is still an open problem for the schemes to control or adjust the dissipation. In this paper, a class of high-order finite difference schemes with minimized dispersion and adaptive dissipation is proposed. As the first step to automatically adjust the dissipation according to the flow structures, we devise a scale sensor to quantify the local length scale of the numerical solution as the effective scaled wavenumber. Then the dispersion-dissipation condition is used to construct the relationship between the dissipation parameter and the effective scaled wavenumber. Thus, we obtain a class of finite difference schemes with adaptive dissipation. To achieve the shock-capturing capability and maintain the superior spectral properties in the smooth regions, we combine the adaptive dissipation scheme with the corresponding weighted essentially non-oscillatory (WENO) scheme to construct a hybrid scheme. At each grid point, either of the sub-schemes is applied dynamically according to a new shock detector.
Keywords:
Adaptive dissipation scheme; Approximate dispersion relation; Hybrid scheme; Low dispersion scheme; Scale sensor; Shock detector

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