9,186 research outputs found
A fourier pseudospectral method for some computational aeroacoustics problems
A Fourier pseudospectral time-domain method is applied to wave propagation problems pertinent to computational aeroacoustics. The original algorithm of the Fourier pseudospectral time-domain method works for periodical problems without the interaction with physical boundaries. In this paper we develop a slip wall boundary condition, combined with buffer zone technique to solve some non-periodical problems. For a linear sound propagation problem whose governing equations could be transferred to ordinary differential equations in pseudospectral space, a new algorithm only requiring time stepping is developed and tested. For other wave propagation problems, the original algorithm has to be employed, and the developed slip wall boundary condition still works. The accuracy of the presented numerical algorithm is validated by benchmark problems, and the efficiency is assessed by comparing with high-order finite difference methods. It is indicated that the Fourier pseudospectral time-domain method, time stepping method, slip wall and absorbing boundary conditions combine together to form a fully-fledged computational algorithm
Sensitivity analysis and determination of free relaxation parameters for the weakly-compressible MRT-LBM schemes
It is well-known that there exist several free relaxation parameters in the
MRT-LBM. Although these parameters have been tuned via linear analysis, the
sensitivity analysis of these parameters and other related parameters are still
not sufficient for detecting the behaviors of the dispersion and dissipation
relations of the MRT-LBM. Previous researches have shown that the bulk
dissipation in the MRT-LBM induces a significant over-damping of acoustic
disturbances. This indicates that MRT-LBM cannot be used to obtain the correct
behavior of pressure fluctuations because of the fixed bulk relaxation
parameter. In order to cure this problem, an effective algorithm has been
proposed for recovering the linearized Navier-Stokes equations from the
linearized MRT-LBM. The recovered L-NSE appear as in matrix form with arbitrary
order of the truncation errors with respect to . Then, in
wave-number space, the first/second-order sensitivity analyses of matrix
eigenvalues are used to address the sensitivity of the wavenumber magnitudes to
the dispersion-dissipation relations. By the first-order sensitivity analysis,
the numerical behaviors of the group velocity of the MRT-LBM are first
obtained. Afterwards, the distribution sensitivities of the matrix eigenvalues
corresponding to the linearized form of the MRT-LBM are investigated in the
complex plane. Based on the sensitivity analysis and the recovered L-NSE, we
propose some simplified optimization strategies to determine the free
relaxation parameters in the MRT-LBM. Meanwhile, the dispersion and dissipation
relations of the optimal MRT-LBM are quantitatively compared with the exact
dispersion and dissipation relations. At last, some numerical validations on
classical acoustic benchmark problems are shown to assess the new optimal
MRT-LBM
Enhancement of shock-capturing methods via machine learning
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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