High-resolution viscous flow simulations at arbitrary Mach number

Briley, W. R.; Taylor, Lafayette K.; Whitfield, David L.

doi:10.1016/s0021-9991(02)00018-9

Cited by 73 publications

(37 citation statements)

References 38 publications

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“…The convective fluxes of the preconditioned governing equations are approximated on the face of a control volume using a formula similar to Roe's flux scheme, as proposed by Briley et al [10]. Consider the surface j of a control volume whose left and right states are denoted by L and R; the numerical flux projected onto the surface can be written as…”

Section: Convective Flux Evaluationmentioning

confidence: 99%

“…Recently, a high-resolution characteristic-based numerical flux approximation for the preconditioned system of hyperbolic equations was developed by Briley et al [10]. The same single-parameter constant matrix similar to the previous work [2] was adopted for the compressible governing equations written in terms of primitive variables.…”

Section: Introductionmentioning

confidence: 99%

“…The same single-parameter constant matrix similar to the previous work [2] was adopted for the compressible governing equations written in terms of primitive variables. A number of validation cases from extremely low Mach numbers to various wall temperature ratios on a flat plate were reported [10]. This global preconditioning based on the free stream Mach number generally provides well-behaved solutions with impressive convergence and accuracy if no rotating flow effect is involved.…”

Section: Introductionmentioning

confidence: 99%

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A Preconditioned Method for Rotating Flows at Arbitrary Mach Number

Sheng

2011

Modelling and Simulation in Engineering

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An improved preconditioning is proposed for viscous flow computations in rotating and nonrotating frames at arbitrary Mach numbers. The key to the current method is the use of both free stream Mach number and rotating Mach number to construct a preconditioning matrix, which is applied to the compressible governing equations written in terms of primitive variables. A Fourier analysis is conducted that reveals the efficacy of the modified preconditioning. Numerical approximations for the convective and diffusive fluxes are detailed based on the preconditioned system of equations. A set of boundary conditions using characteristic variables are described for internal and external flow computations. Numerical validations are performed on four realistic viscous flows in both fixed and rotating frames. The results indicated that the modified preconditioning has a superior performance compared to the original method to predict flows from extremely low to supersonic Mach numbers.

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Section: Convective Flux Evaluationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Preconditioned Method for Rotating Flows at Arbitrary Mach Number

Sheng

2011

Modelling and Simulation in Engineering

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“…The Roe-type flux-difference splitting (FDS) is used by Weiss and Smith [24,[29][30][31][32]. The 3rd-order MUSCL extrapolation is used by Briley et al [33]. The flux-vector splitting (FVS) is applied by Turkle et al [34].…”

Section: Introductionmentioning

confidence: 99%

Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier–Stokes equations

Shen

Zha

2012

Computers & Fluids

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a b s t r a c tA low diffusion E-CUSP (LDE) scheme for preconditioned Navier-Stokes equations is developed. The LDE scheme with high-order WENO reconstruction and high order difference scheme for viscous terms is used to simulate several flows at various speed from low speed natural convection to supersonic flows. The unfactored implicit Gauss-Seidel relaxation scheme, in which the preconditioned Roe's matrices are used, is used for time integration. Numerical results are presented to show efficiency, accuracy and robustness of the new preconditioning scheme.

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“…[5][6][7] For many algorithms preconditioning techniques are a necessity in order to obtain a converged solution at low speeds. [7][8][9][10][11] Another issue…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of liquid sloshing in a partially filled container with inclusion of compressibility effects

Chen¹,

Price²

2009

Physics of Fluids

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A numerical scheme of study is developed to model compressible two-fluid flows simulating liquid sloshing in a partially filled tank. For a two-fluid system separated by an interface as in the case of sloshing, not only a Mach-uniform scheme is required but also an effective way to eliminate unphysical numerical oscillations near the interface. By introducing a preconditioner, the governing equations expressed in terms of primitive variables are solved for both fluids ͑i.e., water, air, gas, etc.͒ in a unified manner. In order to keep the interface sharp and to eliminate unphysical numerical oscillations in unsteady fluid flows, the nonconservative implicit split coefficient matrix method is modified to construct a flux-difference splitting scheme in the dual-time formulation. The proposed numerical model is evaluated by comparisons between numerical results and measured data for sloshing in an 80% filled rectangular tank excited at resonance frequency. Through similar comparisons, the investigation is further extended by examining sloshing flows excited by forced sway motions in two different rectangular tanks with 20% and 83% filling ratios. These examples demonstrate that the proposed method is suitable to capture induced free surface waves and to evaluate sloshing pressure loads acting on the tank walls and ceiling.

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High-resolution viscous flow simulations at arbitrary Mach number

Cited by 73 publications

References 38 publications

A Preconditioned Method for Rotating Flows at Arbitrary Mach Number

A Preconditioned Method for Rotating Flows at Arbitrary Mach Number

Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier–Stokes equations

Numerical simulation of liquid sloshing in a partially filled container with inclusion of compressibility effects

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