In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered gri...In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.展开更多
The computational cost of numerical methods in microscopic-scales such as molecular dynamics(MD) is a deterrent factor that limits simulations with a large number of particles. Hence, it is desirable to decrease the c...The computational cost of numerical methods in microscopic-scales such as molecular dynamics(MD) is a deterrent factor that limits simulations with a large number of particles. Hence, it is desirable to decrease the computational cost and run time of simulations, especially for problems with a symmetrical domain. However, in microscopic-scales, implementation of symmetric boundary conditions is not straightforward. Previously, the present authors have successfully used a symmetry boundary condition to solve molecular flows in constant-area channels. The results obtained with this approach agree well with the benchmark cases. Therefore, it has provided us with a sound ground to further explore feasibility of applying symmetric solutions of micro-fluid flows in other geometries such as variable-area ducts. Molecular flows are solved for the whole domain with and without the symmetric boundary condition. Good agreement has been reached between the results of the symmetric solution and the whole domain solution. To investigate robustness of the proposed method, simulations are conducted for different values of affecting parameters including an external force, a flow density, and a domain length. The results indicate that the symmetric solution is also applicable to variable-area ducts such as micro-nozzles.展开更多
基金supported by the National Natural Science Foundation of China(NSFC)(Grant No. 41074100)the Program for New Century Excellent Talents in University of Ministry of Education of China(Grant No. NCET-10-0812)
文摘In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.
文摘The computational cost of numerical methods in microscopic-scales such as molecular dynamics(MD) is a deterrent factor that limits simulations with a large number of particles. Hence, it is desirable to decrease the computational cost and run time of simulations, especially for problems with a symmetrical domain. However, in microscopic-scales, implementation of symmetric boundary conditions is not straightforward. Previously, the present authors have successfully used a symmetry boundary condition to solve molecular flows in constant-area channels. The results obtained with this approach agree well with the benchmark cases. Therefore, it has provided us with a sound ground to further explore feasibility of applying symmetric solutions of micro-fluid flows in other geometries such as variable-area ducts. Molecular flows are solved for the whole domain with and without the symmetric boundary condition. Good agreement has been reached between the results of the symmetric solution and the whole domain solution. To investigate robustness of the proposed method, simulations are conducted for different values of affecting parameters including an external force, a flow density, and a domain length. The results indicate that the symmetric solution is also applicable to variable-area ducts such as micro-nozzles.
