Simulating unsteady flow phenomena involving moving boundaries is a challenging task,one key requirement of which is a reliable and fast algorithm to deform the computational mesh.Radial basis functions（RBFs） interp...Simulating unsteady flow phenomena involving moving boundaries is a challenging task,one key requirement of which is a reliable and fast algorithm to deform the computational mesh.Radial basis functions（RBFs） interpolation is a very simple and robust method to deform the mesh.However,the number of operations and the requirement of memory storage will be increased rapidly as the number of grid nodes increases,which limits the application of RBFs to three-dimensional（3D） moving mesh.Moving submesh approach（MSA） is an efficient method,but its robustness depends on the method used to deform the background mesh.A hybrid method which combines the benefits of MSA and RBFs interpolation,which is called RBFs-MSA,has been presented.This hybrid method is proved to be robust and efficient via several numerical examples.From the aspect of the quality of deforming meshes,this hybrid method is comparable with the RBFs interpolation;from the aspect of computing efficiency,one test case shows that RBFs-MSA is about two orders of magnitude faster than RBFs interpolation.For these benefits of RBFs-MSA,the new method is suitable for unsteady flow simulation which refers to boundaries movement.展开更多
The probability model is used to analyze the fault tolerance of mesh. To simplify its analysis, it is as-sumed that the failure probability of each node is independent. A 3-D mesh is partitioned into smaller submeshes...The probability model is used to analyze the fault tolerance of mesh. To simplify its analysis, it is as-sumed that the failure probability of each node is independent. A 3-D mesh is partitioned into smaller submeshes,and then the probability with which each submesh satisfies the defined condition is computed. If each submesh satis-fies the condition, then the whole mesh is connected. Consequently, the probability that a 3-D mesh is connected iscomputed assuming each node has a failure probability. Mathematical methods are used to derive a relationship be-tween network node failure probability and network connectivity probability. The calculated results show that the 3-D mesh networks can remain connected with very high probability in practice. It is formally proved that when thenetwork node failure probability is boutded by 0.45 %, the 3-D mesh networks of more than three hundred thousandnodes remain connected with probability larger than 99 %. The theoretical results show that the method is a power-ful technique to calculate the lower bound of the connectivity probability of mesh networks.展开更多
基金Innovation Foundation of CASC(201103)Aeronautical Science Foundation of China(20091488003)
文摘Simulating unsteady flow phenomena involving moving boundaries is a challenging task,one key requirement of which is a reliable and fast algorithm to deform the computational mesh.Radial basis functions（RBFs） interpolation is a very simple and robust method to deform the mesh.However,the number of operations and the requirement of memory storage will be increased rapidly as the number of grid nodes increases,which limits the application of RBFs to three-dimensional（3D） moving mesh.Moving submesh approach（MSA） is an efficient method,but its robustness depends on the method used to deform the background mesh.A hybrid method which combines the benefits of MSA and RBFs interpolation,which is called RBFs-MSA,has been presented.This hybrid method is proved to be robust and efficient via several numerical examples.From the aspect of the quality of deforming meshes,this hybrid method is comparable with the RBFs interpolation;from the aspect of computing efficiency,one test case shows that RBFs-MSA is about two orders of magnitude faster than RBFs interpolation.For these benefits of RBFs-MSA,the new method is suitable for unsteady flow simulation which refers to boundaries movement.
基金Project (69928201) supported by the National Science Fund for Distinguished Young Scholars+1 种基金project (90104028) by the National Natural Science Foundation of China Project by Changjiang Scholar Re-ward Project
文摘The probability model is used to analyze the fault tolerance of mesh. To simplify its analysis, it is as-sumed that the failure probability of each node is independent. A 3-D mesh is partitioned into smaller submeshes,and then the probability with which each submesh satisfies the defined condition is computed. If each submesh satis-fies the condition, then the whole mesh is connected. Consequently, the probability that a 3-D mesh is connected iscomputed assuming each node has a failure probability. Mathematical methods are used to derive a relationship be-tween network node failure probability and network connectivity probability. The calculated results show that the 3-D mesh networks can remain connected with very high probability in practice. It is formally proved that when thenetwork node failure probability is boutded by 0.45 %, the 3-D mesh networks of more than three hundred thousandnodes remain connected with probability larger than 99 %. The theoretical results show that the method is a power-ful technique to calculate the lower bound of the connectivity probability of mesh networks.
