| A. Jameson, Artificial di#usion, upwind biasing, limiters and their e#ect on accuracy and multigrid convergence in transonic and hypersonic flow. AIAA paper 93-3359, Proceedings of the AIAA 11th Computational Fluid Dynamics Conference, Orlando, Florida, July 1993. |
....strategy is based on a multigrid approach. Multigrid methods form the basis of some of the most e#cient available solvers for such problems, both on structured and unstructured grids. For inviscid transonic flow problems, multigrid methods can deliver converged solutions in under 100 cycles [8]. However, for high Reynolds number NavierStokes problems, and for flows involving large regions of low velocity fluid, multigrid convergence rates degrade seriously. This degradation is due partly to the sti#ness induced by the highly stretched grids which are required to resolve e#ciently the ....
A. Jameson, Artificial di#usion, upwind biasing, limiters and their e#ect on accuracy and multigrid convergence in transonic and hypersonic flow. AIAA paper 93-3359, Proceedings of the AIAA 11th Computational Fluid Dynamics Conference, Orlando, Florida, July 1993.
....assure the correct sign to satisfy the LED criterion the flux limiter must now satisfy the additional constraint that #(r) 2. The USLIP formulation is essentially equivalent to standard upwind schemes [142, 185] Both the SLIP and USLIP constructions can be implemented on unstructured meshes [85, 86]. The anti di#usive terms are then calculated by taking the scalar product of the vectors defining an edge with the gradient in the adjacent upstream and downstream cells. 3.4.7. Systems of Conservation Laws: Flux Splitting and Flux Di#erence Splitting. Steger and Warming [182] first showed how ....
.... w j ) Thus these schemes are closely related to schemes which introduce separate splittings of the convective and pressure terms, such as the wave particle scheme [158, 12] the advection upwind splitting method (AUSM) 114, 197] and the convective upwind and split pressure (CUSP) schemes [85]. In order to examine the shock capturing properties of these various schemes, consider the general case of a first order di#usive flux of the form 1 w j ) 34) where the matrix B j determines the properties of the scheme and the scaling factor # j is included for ....
, Artificial di#usion, upwind biasing, limiters and their e#ect on accuracy and multigrid conver51 gence in transonic and hypersonic flows, AIAA paper 93-3359, AIAA 11th Computational Fluid Dynamics Conference, Orlando, FL, July 1993.
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