Title page for ETD etd-11292001-094038

Type of Document Dissertation
Author Wood, William Alfred
Author's Email Address w.a.wood@larc.nasa.gov
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
  • mesh adaption
  • fluctuation splitting
  • CFD
Date of Defense 2001-11-09
Availability unrestricted
A 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

enforced positivity.

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

solution time.

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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