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Non-uniform Grids (non-uniform + grid)
Selected AbstractsA hybrid FVM,LBM method for single and multi-fluid compressible flow problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2010Himanshu Joshi Abstract The lattice Boltzmann method (LBM) has established itself as an alternative approach to solve the fluid flow equations. In this work we combine LBM with the conventional finite volume method (FVM), and propose a non-iterative hybrid method for the simulation of compressible flows. LBM is used to calculate the inter-cell face fluxes and FVM is used to calculate the node parameters. The hybrid method is benchmarked for several one-dimensional and two-dimensional test cases. The results obtained by the hybrid method show a steeper and more accurate shock profile as compared with the results obtained by the widely used Godunov scheme or by a representative flux vector splitting scheme. Additional features of the proposed scheme are that it can be implemented on a non-uniform grid, study of multi-fluid problems is possible, and it is easily extendable to multi-dimensions. These features have been demonstrated in this work. The proposed method is therefore robust and can possibly be applied to a variety of compressible flow situations. Copyright © 2009 John Wiley & Sons, Ltd. [source] Stable high-order finite-difference methods based on non-uniform grid point distributionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2008Miguel Hermanns Abstract It is well known that high-order finite-difference methods may become unstable due to the presence of boundaries and the imposition of boundary conditions. For uniform grids, Gustafsson, Kreiss, and Sundström theory and the summation-by-parts method provide sufficient conditions for stability. For non-uniform grids, clustering of nodes close to the boundaries improves the stability of the resulting finite-difference operator. Several heuristic explanations exist for the goodness of the clustering, and attempts have been made to link it to the Runge phenomenon present in polynomial interpolations of high degree. By following the philosophy behind the Chebyshev polynomials, a non-uniform grid for piecewise polynomial interpolations of degree q,N is introduced in this paper, where N + 1 is the total number of grid nodes. It is shown that when q=N, this polynomial interpolation coincides with the Chebyshev interpolation, and the resulting finite-difference schemes are equivalent to Chebyshev collocation methods. Finally, test cases are run showing how stability and correct transient behaviours are achieved for any degree q Accuracy analysis of super compact scheme in non-uniform grid with application to parabolized stability equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2004V. Esfahanian Abstract A brief derivation of the super compact finite difference method (SCFDM) in non-uniform grid points is presented. To investigate the accuracy of the SCFDM in non-uniform grid points the Fourier analysis is performed. The Fourier analysis shows that the grid aspect ratio plays a crucial role in the accuracy of the SCFDM in a non-uniform grid. It is also found that the accuracy of the higher order relations of the SCFDM is more sensitive to grid aspect ratio than the lower order relations. In addition, to obtain a mathematical representation of the accuracy and making clear the role of the aspect ratio in the accuracy of the SCFDM in non-uniform grids, the modified equation approach is used. For the sake of demonstrating the analytical results obtained from the Fourier analysis and the modified equation approach, the super compact finite difference method is applied to solve the Blasius boundary layer and the non-linear parabolized stability equations as numerical examples indicating the difficulty with non-uniform grid spacing using the super compact scheme. Copyright © 2004 John Wiley & Sons, Ltd. [source] Stable high-order finite-difference methods based on non-uniform grid point distributionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2008Miguel Hermanns Abstract It is well known that high-order finite-difference methods may become unstable due to the presence of boundaries and the imposition of boundary conditions. For uniform grids, Gustafsson, Kreiss, and Sundström theory and the summation-by-parts method provide sufficient conditions for stability. For non-uniform grids, clustering of nodes close to the boundaries improves the stability of the resulting finite-difference operator. Several heuristic explanations exist for the goodness of the clustering, and attempts have been made to link it to the Runge phenomenon present in polynomial interpolations of high degree. By following the philosophy behind the Chebyshev polynomials, a non-uniform grid for piecewise polynomial interpolations of degree q,N is introduced in this paper, where N + 1 is the total number of grid nodes. It is shown that when q=N, this polynomial interpolation coincides with the Chebyshev interpolation, and the resulting finite-difference schemes are equivalent to Chebyshev collocation methods. Finally, test cases are run showing how stability and correct transient behaviours are achieved for any degree q Accuracy analysis of super compact scheme in non-uniform grid with application to parabolized stability equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2004V. Esfahanian Abstract A brief derivation of the super compact finite difference method (SCFDM) in non-uniform grid points is presented. To investigate the accuracy of the SCFDM in non-uniform grid points the Fourier analysis is performed. The Fourier analysis shows that the grid aspect ratio plays a crucial role in the accuracy of the SCFDM in a non-uniform grid. It is also found that the accuracy of the higher order relations of the SCFDM is more sensitive to grid aspect ratio than the lower order relations. In addition, to obtain a mathematical representation of the accuracy and making clear the role of the aspect ratio in the accuracy of the SCFDM in non-uniform grids, the modified equation approach is used. For the sake of demonstrating the analytical results obtained from the Fourier analysis and the modified equation approach, the super compact finite difference method is applied to solve the Blasius boundary layer and the non-linear parabolized stability equations as numerical examples indicating the difficulty with non-uniform grid spacing using the super compact scheme. Copyright © 2004 John Wiley & Sons, Ltd. [source] Applications of transformed-space non-uniform PSTD (TSNU-PSTD) in scattering analysis without the use of the non-uniform FFTMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 1 2003Xiaoping Liu Abstract In this work, we extend the transformed-space, non-uniform pseudo-spectral time domain (TSNU-PSTD) Maxwell solver for a 2D scattering analysis. Prior to implementing the PSTD in this analysis, we first transform the non-uniform grids {xi} and {yj} sampled in the real space for describing complex geometries to uniform ones {ui} and {vj}, in order to fit the dimensions of practical structures and utilize the standard fast Fourier transform (FFT). Next, we use a uniform-sampled, standard FFT to represent spatial derivatives in the space domain of (u, v). It is found that this scheme is as efficient as the conventional uniform PSTD with the computational complexity of O(N log N), since the difference is only the factors of du/dx and dv/dy between the conventional PSTD and the TSNU-PSTD technique. Additionally, we apply an anisotropic version of the Berenger's perfectly matched layers (APML) to suppress the wraparound effect at the open boundaries of the computational domain, which is caused by the periodicity of the FFT. We also employ the pure scattered-field formulation and develop a near-to-far-zone field transformation in order to calculate scattered far fields. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 16,21, 2003 [source] Progress in the Modelling of Air Flow Patterns in Softwood Timber KilnsASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 3-4 2004T.A.G. Langrish Progress in modelling air flow patterns in timber kilns using computational fluid dynamics (CFD) is reviewed in this work. These simulations are intended to predict the distribution of the flow in the fillet spaces between boards in a hydraulic model of a timber kiln. Here, the flow regime between the boards is transitional between laminar and turbulent flow, with Reynolds numbers of the order of 5000. Running the simulation as a transient calculation has shown few problems with convergence issues, reaching a mass residual of 0.2% of the total inflow after 40 to 100 iterations per time step for time steps of 0.01 s. Grid sensitivity studies have shown that non-uniform grids are necessary because of the sudden changes in flow cross section, and the flow simulations are insensitive to grid refinement for non-uniform grids with more than 300,000 cells. The best agreement between the experimentally-measured flow distributions between fillet spaces and those predicted by the simulation have been achieved for (effective) bulk viscosities between the laminar viscosity for water and ten times that value. This change in viscosity is not very large (less than an order of magnitude), given that effective turbulent viscosities are typically several orders of magnitude greater than laminar ones. This result is consistent with the transitional flows here. The effect of weights above the stack can reduce the degree of non-uniformity in air velocities through the stack, especially when thick weights are used, because the stack may then be separated from the eddy at the top of the plenum chamber. [source]
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