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Register a new userVector potential-based MHD solver for non-periodic flows using Fourier continuation expansions
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A high-order method to evolve in time electromagnetic and velocity fields in conducting fluids with non-periodic boundaries is presented. The method has a small overhead compared with fast FFT-based pseudospectral methods in periodic domains. It uses the magnetic vector potential formulation for accurately enforcing the null divergence of the magnetic field, and allowing for different boundary conditions including perfectly conducting walls or vacuum surroundings, two cases relevant for many astrophysical, geophysical, and industrial flows. A spectral Fourier continuation method is used to accurately represent all fields and their spatial derivatives, allowing also for efficient solution of Poisson equations with different boundaries. A study of conducting flows at different Reynolds and Hartmann numbers, and with different boundary conditions, is presented to study convergence of the method and the accuracy of the solenoidal and boundary conditions.
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A high-performance gas kinetic solver using multi-level parallelization is developed to enable pore-scale simulations of rarefied flows in porous media. The Boltzmann model equation is solved by the discrete velocity method with an iterative scheme. The multi-level MPI/OpenMP parallelization is implemented with the aim to efficiently utilise the computational resources to allow direct simulation of rarefied gas flows in porous media based on digital rock images for the first time. The multi-level parallel approach is analyzed in details confirming its better performance than the commonly-used MPI processing alone for an iterative scheme. With high communication efficiency and appropriate load balancing among CPU processes, parallel efficiency of 94% is achieved for 1536 cores in the 2D simulations, and 81% for 12288 cores in the 3D simulations. While decomposition in the spatial space does not affect the simulation results, one additional benefit of this approach is that the number of subdomains can be kept minimal to avoid deterioration of the convergence rate of the iteration process. This multi-level parallel approach can be readily extended to solve other Boltzmann model equations.
Electroconvective flow between two infinitely long parallel electrodes is investigated via a multiphysics computational model. The model solves for spatiotemporal flow properties using two-relaxation-time Lattice Boltzmann Method for fluid and charge transport coupled to Fast Fourier Transport Poisson solver for the electric potential. The segregated model agrees with the previous analytical and numerical results providing a robust approach for modeling electrohydrodynamic flows.
Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newtons equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios, for more complex particles - such as a body with a protrusion - they become unstable. We present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method. Similarly to previous work on this method, the resulting matrix equation in the present approach is solved using a block-LU decomposition. Each step of the block-LU decomposition is modified to incorporate the rigid body dynamics. We show that our method achieves second-order accuracy in space and first-order in time (third-order for practical settings), only with a small additional computational cost to the original method. Our implicit coupling yields stable solution for density ratios as low as $10^{-4}$. We also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method.
A novel hybrid deep neural network architecture is designed to capture the spatial-temporal features of unsteady flows around moving boundaries directly from high-dimensional unsteady flow fields data. The hybrid deep neural network is constituted by the convolutional neural network (CNN), improved convolutional Long-Short Term Memory neural network (ConvLSTM) and deconvolutional neural network (DeCNN). Flow fields at future time step can be predicted through flow fields by previous time steps and boundary positions at those steps by the novel hybrid deep neural network. Unsteady wake flows around a forced oscillation cylinder with various amplitudes are calculated to establish the datasets as training samples for training the hybrid deep neural networks. The trained hybrid deep neural networks are then tested by predicting the unsteady flow fields around a forced oscillation cylinder with new amplitude. The effect of neural network structure parameters on prediction accuracy was analyzed. The hybrid deep neural network, constituted by the best parameter combination, is used to predict the flow fields in the future time. The predicted flow fields are in good agreement with those calculated directly by computational fluid dynamic solver, which means that this kind of deep neural network can capture accurate spatial-temporal information from the spatial-temporal series of unsteady flows around moving boundaries. The result shows the potential capability of this kind novel hybrid deep neural network in flow control for vibrating cylinder, where the fast calculation of high-dimensional nonlinear unsteady flow around moving boundaries is needed.
The general synthetic iteration scheme (GSIS) is extended to find the steady-state solution of nonlinear gas kinetic equation, removing the long-standing problems of slow convergence and requirement of ultra-fine grids in near-continuum flows. The key ingredients of GSIS are that the gas kinetic equation and macroscopic synthetic equations are tightly coupled, and the constitutive relations in macroscopic synthetic equations explicitly contain Newtons law of shear stress and Fouriers law of heat conduction. The higher-order constitutive relations describing rarefaction effects are calculated from the velocity distribution function, however, their constructions are simpler than our previous work (Su et al. Journal of Computational Physics 407 (2020) 109245) for linearized gas kinetic equations. On the other hand, solutions of macroscopic synthetic equations are used to inform the evolution of gas kinetic equation at the next iteration step. A rigorous linear Fourier stability analysis in periodic system shows that the error decay rate of GSIS can be smaller than 0.5, which means that the deviation to steady-state solution can be reduced by 3 orders of magnitude in 10 iterations. Other important advantages of the GSIS are (i) it does not rely on the specific form of Boltzmann collision operator and (ii) it can be solved by sophisticated techniques in computational fluid dynamics, making it amenable to large scale engineering applications. In this paper, the efficiency and accuracy of GSIS is demonstrated by a number of canonical test cases in rarefied gas dynamics.
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