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An efficient three-dimensionasl tructured solver for the Euler and Navier-Stokese quations is developed based on a finite volume upwind algorithm using Roe fluxes. Multigrid and optimal smoothing multi-stage time stepping accelerate convergence. The accuracy of the new solver is demonstrated for inviscid flows in the range 0.675 :5M :5 25. A comparative grid convergence study for transonic turbulent flow about a wing is conducted with the present solver and a scalar dissipation central difference industrial design solver. The upwind solver demonstrates faster grid convergence than the central scheme, producing more consistent estimates of lift, drag and boundary layer parameters. In transonic viscous computations, the upwind scheme with convergence acceleration is over 20 times more efficient than without it. The ability of the upwind solver to compute viscous flows of comparable accuracy to scalar dissipation central schemes on grids of one-quarter the density make it a more accurate, cost effective alternative. In addition, an original convergencea cceleration method termed shock acceleration is proposed. The method is designed to reduce the errors caused by the shock wave singularity M -+ 1, based on a localized treatment of discontinuities. Acceleration models are formulated for an inhomogeneous PDE in one variable. Results for the Roe and Engquist-Osher schemes demonstrate an order of magnitude improvement in the rate of convergence. One of the acceleration models is extended to the quasi one-dimensiona Euler equations for duct flow. Results for this case d monstrate a marked increase in convergence with negligible loss in accuracy when the acceleration procedure is applied after the shock has settled in its final cell. Typically, the method saves up to 60% in computational expense. Significantly, the performance gain is entirely at the expense of the error modes associated with discrete shock structure. In view of the success achieved, further development of the method is proposed

Publisher: Cranfield University

Year: 1995

OAI identifier:
oai:dspace.lib.cranfield.ac.uk:1826/4147

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Cranfield CERES

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- (1989). A class of high-resolution explicit and implicit shock-capturing methods.
- (1992). A comparative study of advanced shockcapturing applied to Burgers' equation.
- (1977). A comparative study of computational methods in cosmic gas dynamics.
- A comparison of numerical flux formulas for the Euler and Navier-Stokes equations. AIAA Paper 87-1104,
- (1993). A comparison of several implicit smoothing methods.
- A contribution to numerical prediction of unsteady flows.
- (1992). A contribution to the great Riernarm solver debate.
- (1977). A finite-volume method for transonic potential flow calculations.
- (1992). A flux splitting scheme with high-resolution and robustness for discontinuities.
- (1993). A generalised Riemann problem for quasi-one-dimensional gas flows.
- (1982). A multiple grid scheme for solving the euler equations.
- (1989). A new multigrid approach to convection problems.
- A systematic comparative study of several high resolution schemes for complex problems in high speed flows.
- (1995). A unified multigrid solver for the Navier-Stokes equations on mixed element meshes.
- a-GMRES: A new parallelizable iterative solver for large sparse non-symmetric linear systems arising from CFD.
- Accurate solution of the 2-D Euler equations with and efficient cell-vertex upwind scheme.
- (1987). Algebraic multigrid.
- (1991). An adaptive grid algorithm for computational shock dynamics.
- An adaptively-refined cartesian mesh solver for the Euler equations.
- (1991). Appendix 5 to GARTEUR AD(AG-15) report -Itesults premsented at the third meeting held at Aerospatiale,
- (1948). Application of a new class of high accuracy TVD schemes to the NavierStokes equations.
- (1987). Application of Wynn's c-algorithm to transonic flow calculations.
- (1981). Approximate IUemann solvers, parameter vectors, and difference schemes.
- (1992). Basins of attraction and the time-dependent approach to obtaining steady-state numerical solutions. Preprint to appear in
- (1990). Blunt-body flow simulations. AIAA Paper 88-2904,1988. [1111
- (1979). Boundary-Layer Theory. McGraw-Hill, seventh edition edition,
- Calculation of plane steady transonic flow.
- (1993). Canonical forms of multidimensional steady inviscid flows.
- (1994). Canonical variables multigrid method for steady-state Euler equations.
- Characteristic decompostion methods for the multidimensional Euler equations.
- Characteristic time-stepping or local preconditioning of the Euler equations.
- Characteristic-based schemes for the Euler equations.
- (1986). Comparison of finite volume flux vector splittings for the Euler equations.
- (1991). Comparison of solution of various Euler solvers and one Navier-Stokes solver for the flow about a sharp-edged cropped delta wing.
- (1984). Compressible Fluid Flow and Systems of Conservation Laws
- Computation of turbulent supersonic flows around pointed bodies having cross-flow separation.
- Computational efficiency achieved by time splitting of finite difference operators.
- Computer-aided analysis of the convergence to steady state of discrete approximations to the Euler equations.
- Condition improvement for point relaxation in multigrid, subsonic Euler-flow computations.
- (1992). Contamination of laminar boundary layers by artifical dissipation in Navier-Stokes solutions.
- (1965). Convergence acceleration methods: The past decade.
- Convergence acceleration through the use of time inclining.
- (1980). Convergence to steadyĆ½-state solutions of the Euler equations on unstructured grids with limiters.
- (1991). Damped direction dependant multigrid for hypersonic flow computations.
- (1995). de Zeeuw. Developments of semi-coarsening and sparse-grid techniques.
- Design of optimally smoothing multi-stage schemes for the Euler equations.
- (1987). Dirichlet boundary conditions for the random-choice method for solving one-dimensional unsteady flows of a perfect gas.
- (1986). Discrete models for the numerical analysis of time-dependent multi-dimensional gas-dynamics.
- Dissipation additions to flux-difference splitting.
- (1991). Dynamical approach study of spurious steady-state numerical s' olutions of nonlinear differential equations, Part I: The ODE connection and its implications for algorithm development in computational fluid dynamics.
- (1991). Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations, Part III: The effects of nonlinear source terms and boundary conditions in reaction-convection equations.
- (1992). Dynamical approach study of spurious steadystate numerical solutions of nonlinear differential equations, Part II: The dynamics of numerics of systems of 2x2 ODEs and its connection to finite discretizations of nonlinear PDEs.
- (1990). Efficient cell-vertex multigrid scheme for the three-dimensional Navier-Stokes equations.
- (1987). Efficient implementation of essentially nonoscillatory shock capturing schemes.
- (1957). Elements of Gas Dynamics.
- (1987). Euler solver for three-dimensional supersonic flows with subsonic pockets.
- (1992). Euler solvers for transonic applications. In NASA 71-ansonic Symposium: Theory, Application and Experiment,
- (1991). Extension of multigrid methodology to supersonic/hypersonic 3-D viscous flows.
- (1987). Extrapolation methods for vector sequences.
- (1993). Finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics.
- (1995). Flux difference splitting techniques for the Euler equations in non-cartesian geometry.
- GMRES acceleration of computational fluid dynamic codes.
- (1986). GMRES: A general minimum residual algorithm for solving nonsymmetric linear systems.
- (1975). High lift aerodynamics.
- Hyperbolic systems of conservation laws and the mathematical theory of shock waves.
- Improved convergence to the steady state of the Euler equations by enhanced wave propagation.
- Modification of quasi-Newton method for nonlinear equa, tions with a sparse jacobian.
- (1985). Multi-Grid Methods and Applications.
- Multi-level adaptive solutions to boundary value problems.
- (1973). Multi-level adaptive technique (MLAT) for fast numerical solution to boundary value problems.
- Multi-stage schemes for the Euler and NavierStokes equations with optimal smoothing.
- (1993). Multigrid calculations of threedimensional viscous cascade flows.
- (1991). Multigrid for hypersonic viscous two- and three-dimensional flows.
- (1982). Multilevel adaptive computations in fluid dynamics.
- (1982). Multiple steady states for 1-D transonic flow. Pre-print, Center for Pure and Applied Mathematics,
- (1991). New light on numerical boundary conditions.
- Newton-like methods for fast high resolution simulation of hypersonic viscous flows.
- Non-reflecting boundary conditions for Euler equation calculations.
- (1993). Nonparametized entropy fix for Roe's method.
- Numerical computation of two-dimensional viscous blunt body flows with an impinging shock.
- Numerical solutions for the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes.
- Numerical wave propagation in an advection equation with a nonlinear source term.
- (1991). On Godunov-type methods for gas dynamics.
- On the estimation of sparse jacobian matrices.
- On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe.
- (1995). Optimal multi-stage schemes for Euler equations with residual smoothing.
- (1991). Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations.
- Preconditioned methods for solving the incompressible and low speed compressible equations.
- (1979). Pressure distribution on the ONERA N16 wing at transonic mach numbers. In AGARD Advisory Report 138. Experimental database for computer program assessment,
- (1992). Private communication,
- (1991). Progress with multigrid schemes for bypersonic flow problems.
- (1990). Recent progress in multidimensional upwinding.
- (1992). Review of preconditioning methods for fluid dynamics.
- (1986). Roe's method in gas dynamical problems associated with the combustion of high-energy solids in a closed tube. College of Aeronautics Report NFP86/18,
- Simple improvements of an upwind TVD scheme for hypersonic flow.
- (1976). Skew upstream differencing schemes for problems involving fluid flow.
- (1985). Some contributions to the modelling of discontinuous flows.
- (1992). Sonic flux formulae.
- Sparse quasi-Newton method for high resolution schemes.
- Sparse quasi-Newton method for Navier-Stokes solutions.
- Stiffness and deflection analysis of complex structures.
- (1994). Surface boundary conditions for the numerical solution of the euler equations.
- (1992). Systems of conservation laws.
- (1988). The behaviour of flux difference splitting schemes near slowly moving shock waves.
- (1983). The evolution of computational methods in aerodynamics.
- The speed of convergence of one iterative process.
- (1980). The use of the Riemann problem in finite difference schemes. In
- Thin layer approximation and algebraic model for separated turbulent flows.
- (1990). Topics in Numerical Computation of Compressible Flow.
- (1979). Towards the ultimate conservative difference scheme V, A second-order sequel to Godunov's method.
- (1993). Turbulence Modelling for CFD. DCW Industries,
- Upwind implicit residual smoothing method for multi-stage schemes.
- (1985). Upwind-difference methods for aerodynamic problems governed by the Euler equations.
- Validation of a multigrid method for the Reynolds averaged equations.
- (1992). Validation of central and upwind 3-D compressible flow solvers.
- Variable coefficient implicit residual smoothing.

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