Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large-scale media. It is necessary to use a nonuniform g...Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large-scale media. It is necessary to use a nonuniform grid, where upsampling the wavefield from the coarse grid to the fine grid is essential for reducing artifacts. In this paper, we suggest a local refinement scheme using the Fourier interpolation, which is superior to traditional interpolation methods since it is theoretically exact if the input wavefield is band limited.Traditional interpolation methods would fail at high upsampling ratios(say 50); in contrast, our scheme still works well in the same situations, and the upsampling ratio can be any positive integer. A high upsampling ratio allows us to greatly reduce the computational burden and memory demand in the presence of tiny structures and large-scale models, especially for 3D cases.展开更多
In the case of lid-driven deep cavity flow, the effects of different resolutions of local grid refinement have been studied in the frame of multiple relaxation times (MRT) lattice Boltzmann method (LBM). In all the ca...In the case of lid-driven deep cavity flow, the effects of different resolutions of local grid refinement have been studied in the frame of multiple relaxation times (MRT) lattice Boltzmann method (LBM). In all the cases, the aspect ratio and Reynolds number are set as 1.5 and 3.200, respectively. First, the applied method is validated by comparing it with two reported works, with which agreements are reached. Then, six separate degrees of local grid refinement at the upper left corner, i.e. purely coarse grid, including 1/64, 1/32, 1/16, 1/8, 1/4 refinements of the lattice number in the width direction have been studied in detail. The results give the following indications:① The refinement degrees lower than 1/8 produce similar results;② For single corner refinement, 1/4 refinement is adequate for clearing the noises in the singularity zone to a large extent;③ New noise around the interface between coarse and fine zones are introduced by local grid refinement. Finally, refinement of entire subzone neighboring the lid is examined to avoid introducing new noises and it has been found effective.展开更多
Predicting rolling bearing fatigue life requires knowledge of the three-dimensional(3D)stress fields in the roller and raceway near the lubricated contact.Owing to the increasingly severe operating conditions,the effe...Predicting rolling bearing fatigue life requires knowledge of the three-dimensional(3D)stress fields in the roller and raceway near the lubricated contact.Owing to the increasingly severe operating conditions,the effect of localized features such as surface roughness,subsurface inclusions,and even the crystallographic structure of the material becomes important.Achieving such detail requires(locally)extremely dense gridding in simulations,which in 3D is a major challenge.Multigrid techniques have been demonstrated to be capable of solving such problems.In this study,multigrid techniques are shown to further increase the efficiency of the solution by exploiting local grid refinement while maintaining the simplicity of a uniform discretization.This is achieved by employing increasingly finer grids only locally,where the highest resolution is required.Results are presented for dry contact and elastohydrodynamically lubricated contact cases,circular as well as elliptic,with varying crystallographic structure,and with surface roughness.The results show that the developed algorithm is very well suited for detailed analysis,with also excellent prospects for computational diagnostics involving actual material crystallographic structure from electron backscatter diffraction measurements.展开更多
We propose an a-posteriori error/smoothness indicator for standard semidiscrete finite volume schemes for systems of conservation laws,based on the numerical production of entropy.This idea extends previous work by th...We propose an a-posteriori error/smoothness indicator for standard semidiscrete finite volume schemes for systems of conservation laws,based on the numerical production of entropy.This idea extends previous work by the first author limited to central finite volume schemes on staggered grids.We prove that the indicator converges to zero with the same rate of the error of the underlying numerical scheme on smooth flows under grid refinement.We construct and test an adaptive scheme for systems of equations in which the mesh is driven by the entropy indicator.The adaptive scheme uses a single nonuniform grid with a variable timestep.We show how to implement a second order scheme on such a space-time non uniform grid,preserving accuracy and conservation properties.We also give an example of a p-adaptive strategy.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.41130418)the National Major Project of China (under grant 2017ZX05008-007)+1 种基金supports from the Youth Innovation Promotion Association CAS (2012054)Foundation for Excellent Member of the Youth Innovation Promotion Association (2016)
文摘Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large-scale media. It is necessary to use a nonuniform grid, where upsampling the wavefield from the coarse grid to the fine grid is essential for reducing artifacts. In this paper, we suggest a local refinement scheme using the Fourier interpolation, which is superior to traditional interpolation methods since it is theoretically exact if the input wavefield is band limited.Traditional interpolation methods would fail at high upsampling ratios(say 50); in contrast, our scheme still works well in the same situations, and the upsampling ratio can be any positive integer. A high upsampling ratio allows us to greatly reduce the computational burden and memory demand in the presence of tiny structures and large-scale models, especially for 3D cases.
基金Supported by Science and Technology Development Planning of Shandong Province,P.R.China(2016GGX104018)
文摘In the case of lid-driven deep cavity flow, the effects of different resolutions of local grid refinement have been studied in the frame of multiple relaxation times (MRT) lattice Boltzmann method (LBM). In all the cases, the aspect ratio and Reynolds number are set as 1.5 and 3.200, respectively. First, the applied method is validated by comparing it with two reported works, with which agreements are reached. Then, six separate degrees of local grid refinement at the upper left corner, i.e. purely coarse grid, including 1/64, 1/32, 1/16, 1/8, 1/4 refinements of the lattice number in the width direction have been studied in detail. The results give the following indications:① The refinement degrees lower than 1/8 produce similar results;② For single corner refinement, 1/4 refinement is adequate for clearing the noises in the singularity zone to a large extent;③ New noise around the interface between coarse and fine zones are introduced by local grid refinement. Finally, refinement of entire subzone neighboring the lid is examined to avoid introducing new noises and it has been found effective.
文摘Predicting rolling bearing fatigue life requires knowledge of the three-dimensional(3D)stress fields in the roller and raceway near the lubricated contact.Owing to the increasingly severe operating conditions,the effect of localized features such as surface roughness,subsurface inclusions,and even the crystallographic structure of the material becomes important.Achieving such detail requires(locally)extremely dense gridding in simulations,which in 3D is a major challenge.Multigrid techniques have been demonstrated to be capable of solving such problems.In this study,multigrid techniques are shown to further increase the efficiency of the solution by exploiting local grid refinement while maintaining the simplicity of a uniform discretization.This is achieved by employing increasingly finer grids only locally,where the highest resolution is required.Results are presented for dry contact and elastohydrodynamically lubricated contact cases,circular as well as elliptic,with varying crystallographic structure,and with surface roughness.The results show that the developed algorithm is very well suited for detailed analysis,with also excellent prospects for computational diagnostics involving actual material crystallographic structure from electron backscatter diffraction measurements.
文摘We propose an a-posteriori error/smoothness indicator for standard semidiscrete finite volume schemes for systems of conservation laws,based on the numerical production of entropy.This idea extends previous work by the first author limited to central finite volume schemes on staggered grids.We prove that the indicator converges to zero with the same rate of the error of the underlying numerical scheme on smooth flows under grid refinement.We construct and test an adaptive scheme for systems of equations in which the mesh is driven by the entropy indicator.The adaptive scheme uses a single nonuniform grid with a variable timestep.We show how to implement a second order scheme on such a space-time non uniform grid,preserving accuracy and conservation properties.We also give an example of a p-adaptive strategy.
