2021
DOI: 10.48550/arxiv.2103.06080
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An exponential integrator/WENO discretization for sonic-boom simulation on modern computer hardware

Abstract: Recently a splitting approach has been presented for the simulation of sonicboom propagation. Splitting methods allow one to divide complicated partial differential equations into simpler parts that are solved by specifically tailored numerical schemes. The present work proposes a second order exponential integrator for the numerical solution of sonic-boom propagation modelled through a dispersive equation with Burgers' nonlinearity. The linear terms are efficiently solved in frequency space through FFT, while… Show more

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Cited by 1 publication
(1 citation statement)
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“…In some problems, for an appropriate choice of A, the action of the matrix function can be computed directly (using FFT techniques). This approach has been used, among others, for kinetic equations (Crouseilles et al 2018;Caliari et al 2021), water waves (Klein & Roidot 2011;Caliari et al 2021), sonic boom propagation (Einkemmer et al 2021), and the simulation of Bose-Einstein condensates (Besse et al 2017). However, due to the fully nonlinear nature and the fundamentally complex structure of the MHD equations, such an approach is not feasible.…”
Section: Exponential Integrators: Efficient Matrix-free Implementationmentioning
confidence: 99%
“…In some problems, for an appropriate choice of A, the action of the matrix function can be computed directly (using FFT techniques). This approach has been used, among others, for kinetic equations (Crouseilles et al 2018;Caliari et al 2021), water waves (Klein & Roidot 2011;Caliari et al 2021), sonic boom propagation (Einkemmer et al 2021), and the simulation of Bose-Einstein condensates (Besse et al 2017). However, due to the fully nonlinear nature and the fundamentally complex structure of the MHD equations, such an approach is not feasible.…”
Section: Exponential Integrators: Efficient Matrix-free Implementationmentioning
confidence: 99%