期刊
THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS
卷 34, 期 4, 页码 483-496出版社
SPRINGER
DOI: 10.1007/s00162-020-00531-1
关键词
Shock capturing; Machine learning; Fluid mechanics
资金
- National Science Foundation Graduate Research Fellowship [1745301]
In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the development of an improved finite-volume method for simulating PDEs with discontinuous solutions. Shock-capturing methods make use of nonlinear switching functions that are not guaranteed to be optimal. Because data can be used to learn nonlinear relationships, we train a neural network to improve the results of a fifth-order WENO method. We post-process the outputs of the neural network to guarantee that the method is consistent. The training data consist of the exact mapping between cell averages and interpolated values for a set of integrable functions that represent waveforms we would expect to see while simulating a PDE. We demonstrate our method on linear advection of a discontinuous function, the inviscid Burgers' equation, and the 1-D Euler equations. For the latter, we examine the Shu-Osher model problem for turbulence-shock wave interactions. We find that our method outperforms WENO in simulations where the numerical solution becomes overly diffused due to numerical viscosity.
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