A new approximate LU factorization scheme for the Reynolds-averaged Navier-Stokes equations

Pan, Dartzi; Lomax, Harvard

doi:10.2514/6.1986-337

Cited by 16 publications

(17 citation statements)

References 4 publications

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“…To achieve a second-order accurate solution in space, a piecewise linear model for the stored cell centre variables is used in conjunction with a slope limiter to prevent over-shoots or under-shoots in the interpolated data at cell interfaces before the two Riemann states are computed. At the pseudo-time iteration level, however, a first order upwind scheme is sufficient to calculate the inviscid fluxes and the resultant linear equations are solved using an approximate LU factorisation scheme [55]. At every real time step, once the flow variables including density have been calculated, the position of the material interface can be defined as the contour with the average density value of the two fluids.…”

Section: Free Surface Capturing Methodsmentioning

confidence: 99%

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Estudo do Galgamento de Estruturas Marítimas utilizando um Modelo Numérico baseado na Teoria da Onda em Condições de Água pouco Profunda

Reis¹,

Neves²

2010

RGCI

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The main objective of Workpackage 5 is to use numerical simulation of wave overtopping in order to solve the problem of suspected scale effects. A second, related, objective is to improve existing codes in such a way as they are able to simulate wave overtopping in a reliable way. The final, single, objective is to numerically model long waves on the shallow foreshore at Petten in order to understand the phenomenon of long waves and their effect on overtopping. This report deals with the work undertaken towards the first two objectives, the simulations undertaken for objective 3 are the subject of a separate report entitled "Influence of low-frequency waves on wave overtopping" by M.R.A. van Gent and C.C. Giarrusso and published by WL | Delft hydraulics in November 2003.Realistic simulations of wave overtopping require numerical methods which are able accurately to simulate the shoaling, breaking and possible overturning of waves prior to their impact on the seawall. It is a further requirement that the simulation continues after impact, modelling the formation of the overtopping jet and the reflection of the wave. The research groups at Manchester Metropolitan University (MMU) and the University of Gent (UGent) have been working in parallel on the development of such numerical codes. The MMU code, AMAZON-SC, is a numerical wave flume based on the free surface capturing approach. While the UGent code, LVOF, is a numerical wave basin based on the volume of fluid approach. This report describes the progress of these numerical methods, in order to address the first two objectives of Workpackage 5. Their application to various cases, is also discussed, including: a test problem involving wave overtopping of a smooth sea-dike, wave overtopping at Samphire Hoe and an investigation of scale effects on rough impermeable structures.The Report begins with a general introduction, followed by a section describing AMAZON-SC (the MMU code), a section describing LVOF (the UGent code) and then some general conclusions.

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Section: Free Surface Capturing Methodsmentioning

confidence: 99%

“…Each of the elements in D, L and U is a 4 × 4 matrix. An approximate LU factorisation(ALU) scheme as proposed by Pan and Lomax [55] can be adopted to form the inverse of (16) in the form…”

Section: Wp5: Numerical Modelling Clash -Evk3-ct-2001-00058mentioning

confidence: 99%

Estudo do Galgamento de Estruturas Marítimas utilizando um Modelo Numérico baseado na Teoria da Onda em Condições de Água pouco Profunda

Reis¹,

Neves²

2010

RGCI

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“…Each of the elements in D, L and U An approximate LU factorization (AL Pan and Lomax [19] can be adopted to obtain erse of equation (10) in the form is a 5 5  matrix. U) scheme as proposed by the inv…”

Section: Numerical Solutionmentioning

confidence: 99%

Numerical Simulation of Water Impact on a Wave Energy Converter in Free Fall Motion

Hu¹,

Causon²,

Mingham³

et al. 2013

OJFD

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Results are presented for the 3D numerical simulation of the water impact of a wave energy converter in free fall and subsequent heave motion. The solver, AMAZON-3D, employs a Riemann-based finite volume method on a Cartesian cut cell mesh. The computational domain includes both air and water regions with the air/water boundary captured automatically as a discontinuity in the density field thereby admitting break up and recombination of the free surface. Temporal discretisation uses the artificial compressibility method and a dual time stepping strategy. Cartesian cut cells are used to provide a boundary-fitted grid at all times. The code is validated by experimental data including the free fall of a cone and free decay of a single Manchester Bobber component.

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“…An approximate LU factorization scheme (Pan & Lomax 1988) is adopted for equation (3.23), and the inverse of the equation can be written as …”

Section: (C ) the Dual Time-stepping Techniquementioning

confidence: 99%

An improved free surface capturing method based on Cartesian cut cell mesh for water-entry and -exit problems

Wang

2009

Proc. R. Soc. A.

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The free surface capturing method based on Cartesian cut cell mesh is extended to the water-entry and -exit fields with body-fluid interaction. The governing equations are the incompressible Euler equations for a variable density fluid system with a free surface, which is treated as a contact discontinuity. The solver is based on the artificial compressibility method with a dual time-stepping technique for time advancing and the finite-volume method with a high-resolution Godunov-type upwind scheme on spatial discretization. For solving the numerical problem caused by the extension, the acceleration term of body is introduced for the new pressure condition of moving solid boundary, and the exact Riemann solution is used to calculate the flux of the solid boundary. In addition, a new solution of gradients based on the least-squares idea is presented for simply calculating the gradients. Finally, test cases show that the present method is available and can be successfully applied in various water-entry and -exit phenomena.

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A new approximate LU factorization scheme for the Reynolds-averaged Navier-Stokes equations

Cited by 16 publications

References 4 publications

Estudo do Galgamento de Estruturas Marítimas utilizando um Modelo Numérico baseado na Teoria da Onda em Condições de Água pouco Profunda

Estudo do Galgamento de Estruturas Marítimas utilizando um Modelo Numérico baseado na Teoria da Onda em Condições de Água pouco Profunda

Numerical Simulation of Water Impact on a Wave Energy Converter in Free Fall Motion

An improved free surface capturing method based on Cartesian cut cell mesh for water-entry and -exit problems

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