High-resolution upwind schemes for the three-dimensional incompressible Navier-Stokes equations
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Hartwich, Peter M.↗
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Hsu, Chung-Hao
Publications and source records attributed to Hsu, Chung-Hao.
Total Variation Diminishing (TVD) schemes of uniform accuracy
Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.
Hartwich, PETER-M.↗
Incompressible Navier-Stokes computations of vortical flows over double-delta wings
An implicit flux-difference splitting scheme is used to compute incompressible laminar vortical flows about a thin round-edged double-delta wing with 80 deg and 60 deg leading-edged sweep for the strake and the main wing respectively. The numerical scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. It is second-order accurate spatially by applying TVD-like upwind discretization to the inviscid fluxes and central differencing to the viscous shear fluxes. The interaction between the two primary vortices emanating from the apex and kink leading-edges is successfully simulated. The computed trajectories of vortical cores compare well with experimental data.
Hsu, Chung-Hao↗
Incompressible Navier-Stokes solutions for a sharp-edged double-delta wing
An implicit finite-difference scheme is used to compute the incompressible laminar vortical flow around a double-delta wing with an aspect ratio of 2.06. By adding a time derivative of the pressure to the continuity equation, the unsteady incompressible Navier-Stokes equations can be integrated like a conventional parabolic time-dependent system of equations. The flux-difference split scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. The trajectory of the vortical core is well predicted in comparison with experimental data.
Hsu, Chung-Hao↗
High resolution upwind schemes for the three-dimensional incompressible Navier-Stokes equations
Based on flux-difference splitting, implicit high resolution schemes are constructed for efficient computations of steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. These schemes use first-order accurate Euler backward-time differencing and second-order central differencing for the viscous shear fluxes. Up to third-order accurate upwind differencing is achieved through a reconstruction of the solution from its cell averages. The reconstruction is accomplished by linear interpolation, where the node stencils are selected such that in regions of smooth solution the flow is highly resolved while spurious oscillations in regions of rapid changes in gradient are still suppressed. Fairly rapid convergence to steady-state solutions is attained with a completely vectorizable hybrid time-marching method. Flows around a sharp-edged delta wing are computed with the maximum accuracy of the upwind-differencing restricted to first-, second-, and third-order, to illustrate the effect of accuracy on the global and on the local vortical flow fields. The results are validated with experimental data.
Hartwich, PETER-M.↗
Three-dimensional incompressible Navier-Stokes simulations of slender-wing vortices
The application of an implicit flux-difference splitting scheme to leading-edge vortex flows is described. The numerical scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. Second-order spatial accuracy is achieved by applying TVD-like upwind discretization to the inviscid fluxes and central differencing to the viscous shear fluxes. Good agreement between computed results and experimental data has been obtained for three different low-aspect-ratio wings.
Hsu, Chung-Hao↗