Type of Document Dissertation Author Wood, William Alfred Author's Email Address firstname.lastname@example.org URN etd-11292001-094038 Title Multi-dimensional Upwind Fluctuation Splitting Scheme with Mesh Adaption for Hypersonic Viscous Flow Degree PhD Department Aerospace and Ocean Engineering Advisory Committee
Advisor Name Title Grossman, Bernard M. Committee Chair Barnwell, Richard W. Committee Member Gnoffo, Peter A. Committee Member Schetz, Joseph A. Committee Member Walters, Robert W. Committee Member Keywords
- mesh adaption
- fluctuation splitting
Date of Defense 2001-11-09 Availability unrestricted AbstractA multi-dimensional upwind fluctuation splitting scheme is developed and
implemented for two-dimensional and axisymmetric formulations of the
Navier-Stokes equations on unstructured meshes.
Key features of the scheme are the compact stencil, full upwinding, and
non-linear discretization which allow for second-order accuracy with
Throughout, the fluctuation splitting scheme is compared to a current
state-of-the-art finite volume approach, a second-order, dual mesh
upwind flux difference splitting scheme (DMFDSFV), and is shown to
produce more accurate results using fewer computer resources for a wide
range of test cases.
The scalar test cases include advected shear, circular advection,
non-linear advection with coalescing shock and expansion fans, and
For all scalar cases the fluctuation splitting scheme is more accurate,
and the primary mechanism for the improved fluctuation splitting
performance is shown to be the reduced production of artificial
dissipation relative to DMFDSFV.
The most significant scalar result is for combined advection-diffusion,
where the present fluctuation splitting scheme is able to resolve the
physical dissipation from the artificial dissipation on a much coarser
mesh than DMFDSFV is able to, allowing order-of-magnitude reductions in
Among the inviscid test cases the converging supersonic streams problem
is notable in that the fluctuation splitting scheme exhibits
superconvergent third-order spatial accuracy.
For the inviscid cases of a supersonic diamond airfoil, supersonic
slender cone, and incompressible circular bump the fluctuation splitting
drag coefficient errors are typically half the DMFDSFV drag errors.
However, for the incompressible inviscid sphere the fluctuation
splitting drag error is larger than for DMFDSFV.
A Blasius flat plate viscous validation case reveals a more accurate
vertical-velocity profile for fluctuation splitting, and the reduced
artificial dissipation production is shown relative to DMFDSFV.
Remarkably the fluctuation splitting scheme shows grid converged skin friction
coefficients with only five points in the boundary layer for this case.
A viscous Mach 17.6 (perfect gas) cylinder case demonstrates solution
monotonicity and heat transfer capability with the fluctuation splitting
While fluctuation splitting is recommended over DMFDSFV, the difference
in performance between the schemes is not so great as to obsolete DMFDSFV.
The second half of the dissertation develops a local, compact,
anisotropic unstructured mesh adaption scheme in conjunction with the
multi-dimensional upwind solver, exhibiting a characteristic alignment
behavior for scalar problems.
This alignment behavior stands in contrast to the curvature clustering
nature of the local, anisotropic unstructured adaption strategy based
upon a posteriori error estimation that is used for comparison.
The characteristic alignment is most pronounced for linear advection,
with reduced improvement seen for the more complex non-linear advection
and advection-diffusion cases.
The adaption strategy is extended to the two-dimensional and axisymmetric
Navier-Stokes equations of motion through the concept of fluctuation
The system test case for the adaption strategy is a sting mounted
capsule at Mach-10 wind tunnel conditions, considered in both
two-dimensional and axisymmetric configurations.
For this complex flowfield the adaption results are disappointing
since feature alignment does not emerge from the local operations.
Aggressive adaption is shown to result in a loss of robustness for the
solver, particularly in the bow shock/stagnation point interaction
Reducing the adaption strength maintains solution robustness but fails
to produce significant improvement in the surface heat transfer
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