An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds-averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open-source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR-F6 wing-body-nacelle-pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times. 相似文献
In this paper, we present an approach of dynamic mesh adaptation for simulating complex 3‐dimensional incompressible moving‐boundary flows by immersed boundary methods. Tetrahedral meshes are adapted by a hierarchical refining/coarsening algorithm. Regular refinement is accomplished by dividing 1 tetrahedron into 8 subcells, and irregular refinement is only for eliminating the hanging points. Merging the 8 subcells obtained by regular refinement, the mesh is coarsened. With hierarchical refining/coarsening, mesh adaptivity can be achieved by adjusting the mesh only 1 time for each adaptation period. The level difference between 2 neighboring cells never exceeds 1, and the geometrical quality of mesh does not degrade as the level of adaptive mesh increases. A predictor‐corrector scheme is introduced to eliminate the phase lag between adapted mesh and unsteady solution. The error caused by each solution transferring from the old mesh to the new adapted one is small because most of the nodes on the 2 meshes are coincident. An immersed boundary method named local domain‐free discretization is employed to solve the flow equations. Several numerical experiments have been conducted for 3‐dimensional incompressible moving‐boundary flows. By using the present approach, the number of mesh nodes is reduced greatly while the accuracy of solution can be preserved. 相似文献
We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point. 相似文献
The dependence of the beam propagation factor (M2 parameter) with the absorbed pump power in the case of monolithic microchip laser under face-cooled configuration is extensively
studied. Our investigations show that the M2 parameter is related to the absorbed pump power through two parameters (α and β) whose values depend on the laser material properties and laser configuration. We have shown that one parameter arises due
to the oscillation of higher order modes in the microchip cavity and the other parameter accounts for the spherical aberration
associated with the thermal lens induced by the pump beam. Such dependency of M2 parameter with the absorbed pump power is experimentally verified for a face-cooled monolithic microchip laser based on Nd3+ -doped GdVO4 crystal and the values of α and β parameters were estimated from the experimentally measured data points. 相似文献
Several promising approaches for hexahedral mesh generation work as follows: Given a prescribed quadrilateral surface mesh they first build the combinatorial dual of the hexahedral mesh. This dual mesh is converted into the primal hexahedral mesh, and finally embedded and smoothed into the given domain. Two such approaches, the modified whisker weaving algorithm by Folwell and Mitchell, as well as a method proposed by the author, rely on an iterative elimination of certain dual cycles in the surface mesh. An intuitive interpretation of the latter method is that cycle eliminations correspond to complete sheets of hexahedra in the volume mesh.
Although these methods can be shown to work in principle, the quality of the generated meshes heavily relies on the dual cycle structure of the given surface mesh. In particular, it seems that difficulties in the hexahedral meshing process and poor mesh qualities are often due to self-intersecting dual cycles. Unfortunately, all previous work on quadrilateral surface mesh generation has focused on quality issues of the surface mesh alone but has disregarded its suitability for a high-quality extension to a three-dimensional mesh.
In this paper, we develop a new method to generate quadrilateral surface meshes without self-intersecting dual cycles. This method reuses previous b-matching problem formulations of the quadrilateral mesh refinement problem. The key insight is that the b-matching solution can be decomposed into a collection of simple cycles and paths of multiplicity two, and that these cycles and paths can be consistently embedded into the dual surface mesh.
A second tool uses recursive splitting of components into simpler subcomponents by insertion of internal two-manifolds. We show that such a two-manifold can be meshed with quadrilaterals such that the induced dual cycle structure of each subcomponent is free of self-intersections if the original component satisfies this property. Experiments show that we can achieve hexahedral meshes with a good quality. 相似文献
Let
d−1{(x1,…,xd)
d:x21+···+x2d=1} be the unit sphere of the d-dimensional Euclidean space
d. For r>0, we denote by Brp (1p∞) the class of functions f on
d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on
d−1,
and Pλk(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of Brp in Lq(
d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces XN of Lq(
d−1).The main result in this paper is that for r2(d−1)2,where ANBN means that there exists a positive constant C, independent of N, such that C−1ANBNCAN.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions. 相似文献