Nonlinear relaxation Navier-Stokes solver for three-dimensional, high-speed internal flows
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Edwards, Jack R.↗
Engineering topics
Mcrae, D. S.
Publications and source records attributed to Mcrae, D. S..
An efficient nonlinear relaxation technique for the three-dimensional, Reynolds-averaged Navier-Stokes equations
An efficient implicit method for the computation of steady, three-dimensional, compressible Navier-Stokes flowfields is presented. A nonlinear iteration strategy based on planar Gauss-Seidel sweeps is used to drive the solution toward a steady state, with approximate factorization errors within a crossflow plane reduced by the application of a quasi-Newton technique. A hybrid discretization approach is employed, with flux-vector splitting utilized in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes. Convergence histories and comparisons with experimental data are presented for several 3-D shock-boundary layer interactions. Both laminar and turbulent cases are considered, with turbulent closure provided by a modification of the Baldwin-Barth one-equation model. For the problems considered (175,000-325,000 mesh points), the algorithm provides steady-state convergence in 900-2000 CPU seconds on a single processor of a Cray Y-MP.
Edwards, Jack R.↗
Nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations
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Edwards, Jack R.↗
A coarse-grid correction/nonlinear relaxation algorithm for the three-dimensional, compressible Navier-Stokes equations
A combined coarse-grid correction/upwind relaxation strategy to provide rapid convergence for 3D high-speed viscous flowfields is discussed an evaluated. The construction and analysis of a simple two-grid acceleration procedure based on 'hyperbolic' multigrid concepts is presented. Numerical simulations of a 2D compression-corner flowfield, a 3D crossing shock/turbulent boundary layer interaction, and a 3D scramjet inlet flowfield are presented to illustrate the benefits of the approach. Results indicate that the procedure generally converges two or more times faster than the baseline algorithm.
Edwards, Jack R.↗
Time-accurate simulation of a self-excited oscillatory supersonic external flow with a multi-block solution-adaptive mesh algorithm
Results are presented of an investigation of the time-accurate simulation of supersonic unsteady flow oscillations over spike-tipped bodies using the multistage Runge-Kutta scheme coupled with a dynamic solution-adaptive grid algorithm modified for multiblock capabilities. The inviscid fluxes are described by a modified advective upwind split method to obviate the need for artificial dissipation. If a time-varying, solution-adaptive mesh algorithm is incorporated, resolution of the details of the unsteady spike-tipped body flow is improved. The adaptive algorithm is also shown to resolve multiple and diverse features of the flow simultaneously, with the adapted regions in the mesh convecting with these features as they translate.
Ingram, Clint L.↗
A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations
A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.
Edwards, Jack R.↗
Numerical simulations using a dynamic solution-adaptive grid algorithm, with applications to unsteady internal flows
An investigation into the numerical simulation of unsteady flows is undertaken using a two-stage Runge-Kutta scheme coupled with the dynamic solution-adaptive grid algorithm developed by the authors. The inviscid fluxes are described by a modified Advective Upwind Split Method to eliminate the need for artificial dissipation. A well-documented numerical example containing moving discontinuities is presented that demonstrates the ability of the coupled grid/solver scheme to accurately capture unsteady flowfield phenomena. Applications are to a typical inlet diffuser configuration at Mach 3.0 with excessive back pressure inducing inlet unstart.
Benson, Rusty A.↗
A solution-adaptive mesh algorithm for dynamic/static refinement of two and three dimensional grids
An adaptive grid algorithm has been developed in two and three dimensions that can be used dynamically with a solver or as part of a grid refinement process. The algorithm employs a transformation from the Cartesian coordinate system to a general coordinate space, which is defined as a parallelepiped in three dimensions. A weighting function, independent for each coordinate direction, is developed that will provide the desired refinement criteria in regions of high solution gradient. The adaptation is performed in the general coordinate space and the new grid locations are returned to the Cartesian space via a simple, one-step inverse mapping. The algorithm for relocation of the mesh points in the parametric space is based on the center of mass for distributed weights. Dynamic solution-adaptive results are presented for laminar flows in two and three dimensions.
Benson, Rusty A.↗
Nonlinear truncation error analysis of finite difference schemes for the Euler equations
It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.
Klopfer, G. H.↗
Numerical simulation of viscous-inviscid interactions on indented nose tips
An implicit numerical algorithm to solve the unsteady thin-layer Navier-Stokes equations in a strong conservative form has been used to compute the viscous flow over indented nose tips placed in a supersonic free stream. Numerical solutions are presented for axisymmetric and three-dimensional indented configurations for laminar flow conditions. Results demonstrate the capability of the present numerical procedure to predict flow fields that contain strong viscous-inviscid interactions, including boundary-layer separation, reattachment, and embedded discontinuities. Comparisons with available experimental data for the shock shape and surface pressure are also given.
Rizk, Y. M.↗
Computation of hypersonic viscous flow around three-dimensional bodies at high angles of attack
A parabolized Navier-Stokes code capable of predicting steady viscous supersonic flows with cross-flow separation is applied to three-dimensional arbitrary geometries at high angles of attack. The numerical procedure, which is implicit, noniterative, and of second-order accuracy in the marching direction, has been used to compute complicated flow fields containing a relatively thick sonic layer and regions of strong viscous-inviscid interaction. A consistent and accurate procedure has also been developed to provide the necessary starting data through timewise integration of the equations of motion near the nose-tip region of the body. Numerical results obtained from the present method compare well with experiment for both the surface pressures and heat transfer.
Rizk, Y. M.↗
Flight experiments with a slender cone at angle of attack
The three-dimensional leeward separation about a 5 deg semi-angle cone at an 11 deg angle of attack was investigated in flight, in the wind tunnel, and by numerical computations. The test conditions were Mach numbers of 0.6, 1.5, and 1.8 at Reynolds numbers between 7 and 10 million based on free-stream conditions and a 30-inch wetted length or surface. The surface conditions measured included mean static and fluctuating pressures; skin friction magnitudes and separation line positions were obtained using obstacle blocks. The mean static pressures from flight and wind tunnel were in good agreement. The computed results gave the same distributions, but were slightly more positive in magnitude. The experimentally measured primary and secondary separation line locations compared closely with computed results. There were substantial differences in level and in trend between the surface root-mean-square pressure fluctuations obtained in flight and in the wind tunnel, due, it is thought, to a relatively high acoustic disturbance level in the tunnel compared with the quiescent conditions in flight.
Peake, D. J.↗
The nonlinear modified equation approach to analyzing finite difference schemes
The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.
Klopfer, G. H.↗
A computational and experimental study of high Reynolds number viscous/inviscid interaction about a cone at high angle of attack
The flow over a 5 deg semi-angle cone at incidence in supersonic flow is studied as a model problem for the flow over aircraft forebodies. A computational method utilizing the conically symmetric Navier-Stokes equations is used to obtain theoretical flow results which are compared with experimental data from the Ames Research Center 6- by 6-Foot Wind Tunnel and with results from a cone model sting mounted on an F-15 aircraft. The computed results agree well with the wind-tunnel data but less well with the flight data. Modification of the algebraic turbulence model was necessary to reflect an apparent lower turbulence level in flight than was present in the wind tunnel.
Mcrae, D. S.↗
Numerical simulation of supersonic cone flow at high angle of attack
A conical symmetry assumption is applied to the full Navier-Stokes equations resulting in an equation set containing time and two coordinate directions as independent variables. The set is integrated by use of a finite difference technique for the particular case of sharp cones at incidence. Solutions are obtained and compared with experiment for auxiliary conditions corresponding to both laminar and turbulent flows. Closure for the turbulent flow case is provided by use of a scalor eddy viscosity model based on the mixing length hypothesis. Modifications to the eddy viscosity model were found which led to excellent surface pressure and surface flow direction agreement for turbulent flow at low supersonic Mach numbers. It is apparent that further work on the turbulence model is necessary for agreement at higher supersonic Mach numbers.
Mcrae, D. S.↗
Supersonic viscous flow over cones at incidence
The conically symmetric Navier-Stokes equations are solved by MacCormack's method for the supersonic flow past sharp cones at incidence. To provide closure for the case of turbulent flows, a scalar eddy-viscosity model based on mixing length hypotheses is used. The results are compared with available experimental data.
Mcrae, D. S.↗