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doi: 10.1002/fld.1650180802pmid: N/A
The generalized integral transform technique is applied to the boundary layer equations for flow over a sphere in their primitive variables. Even though a diffusion‐based eigenvalue problem is used, the velocity profile, shear stress and separation point have been calculated with high accuracy. Low‐order approximations are shown to be accurate near the surface and the predictions of the separation point is very good. Comparison with finite difference results shows the better convergence behaviour of the integral transform method.
doi: 10.1002/fld.1650180803pmid: N/A
A penalty function, finite volume method is described for two‐dimensional laminar and turbulent flows. Turbulence is modelled using the k‐ϵ model. The governing equations are discretized and the resulting algebraic equations are solved using both sequential and coupled methods. The performance of these methods is gauged with reference to a tuned SIMPLE‐C algorithm. Flows considered are a square cavity with a sliding top, a plane channel flow, a plane jet impingement and a plane channel with a sudden expansion. A sequential method is employed, which uses a variety of dicretization practices, but is found to be extremely slow to converge; a coupled method, evaluated using a variety of matrix solvers, converges rapidly but, relative to the sequential approach, requires larger memory.
doi: 10.1002/fld.1650180804pmid: N/A
The work outlined below presents simple but effective adaptive meshing algorithms for boundary integral methods modelling inviscid flows (panel method) using the IGES standard for describing geometry. By using certain IGES entities in describing the boundary, CAD‐derived geometry may be used such that the geometric integrity of the boundary is maintained after an adaptive redistribution of the mesh. Three types of error estimators are tested and all are shown to produce a more accurate representation of the flow phenomena for the same number of panels as compared with a uniform mesh distribution.
doi: 10.1002/fld.1650180805pmid: N/A
An efficient numerical method is presented for solving the equations of motion for viscous fluids. The equations are discretized on the basis of unstructured finite element meshes and then solved by direct iteration. Advective fluxes are temporarily fixed at each iteration to provide a linearized set of coupled equations which are then also solved by iteration using a fully implicit algebraic multigrid (AMG) scheme. A rapid convergence to machine accuracy is achieved that is almost mesh‐independent. The scaling of computing time with mesh size is therefore close to the optimum.
doi: 10.1002/fld.1650180806pmid: N/A
The two‐dimensional incompressible Navier‐Stokes equations in primitive variables have been solved by a pseudospectral Chebyshev method using a semi‐implicit fractional step scheme. The latter has been adapted to the particular features of spectral collocation methods to develop the monodomain algorithm. In particular, pressure and velocity collocated on the same nodes are sought in a polynomial space of the same order; the cascade of scalar elliptic problems arising after the spatial collocation is solved using finite difference preconditioning. With the present procedure spurious pressure modes do not pollute the pressure field. As a natural development of the present work a multidomain extent was devised and tested. The original domain is divided into a union of patching sub‐rectangles. Each scalar problem obtained after spatial collocation is solved by iterating by subdomains. For steady problems a C1 solution is recovered at the interfaces upon convergence, ensuring a spectrally accurate solution. A number of test cases have been solved to validate the algorithm in both its single‐block and multidomain configurations. The preliminary results achieved indicate that collocation methods in multidomain configurations might become a viable alternative to the spectral element technique for accurate flow prediction.
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