Abstract
Recently a splitting approach has been presented for the simulation of sonic-boom 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 the nonlinear terms are efficiently solved by a WENO scheme. The numerical method is designed to be highly parallelisable and therefore takes full advantage of modern computer hardware. The new approach also improves the accuracy compared to the splitting method and it reduces oscillations. The enclosed numerical results illustrate that parallelisation on a CPU results in a speedup of 22 times faster than the straightforward sequential version. The GPU implementation further accelerates the runtime by a factor 3, which improves to 5 when single precision is used instead of double precision.
Highlights
Sonic-booms are acoustic waves generated by supersonic planes when they fly faster than the speed of sound
The need arises to perform numerical simulations that aim to model the propagation of acoustic waves generated by supersonic planes
In this paper we introduce a new approach based on exponential integrators to solve efficiently the aforementioned partial differential equation
Summary
Sonic-booms are acoustic waves generated by supersonic planes when they fly faster than the speed of sound. In this paper we consider only the second problem, which is of key importance in any optimization algorithm as the final goal is to model the shape of the aircraft in such a way that N -waves do not appear or are mitigated by the time that sonic-booms reach the ground. This turns into modelling the sonic-boom propagation through a partial differential equation and solving it several times.
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