A projection method for combustion in the zero Mach number limit

Lai, M. C.; Bell, John B.; Colella, P.

doi:10.2514/6.1993-3369

Cited by 47 publications

(77 citation statements)

References 8 publications

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“…A similar Poisson equation with variable coefficient was solved by Bell and Marcus [11] to impose the divergence-free constraint for variable-density flows-see also [12,13].…”

Section: Scheme In Non-conservative Form: Advscmentioning

confidence: 99%

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Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Nicoud¹

2000

Journal of Computational Physics

164

149

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Three finite-difference algorithms are proposed to solve a low-Mach number approximation for the Navier-Stokes equations. These algorithms exhibit fourth-order spatial and second-order temporal accuracy. They are dissipation-free, and thus well suited for DNS and LES of turbulent flows. The key ingredient common to each of the methods presented is a Poisson equation with variable coefficient that is solved for the hydrodynamic pressure. This feature ensures that the velocity field is constrained correctly. It is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation. An existing set of finite-difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation through the non-linear convective terms. An algorithm which conserves mass, momentum, and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one. Results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms.

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“…A similar Poisson equation with variable coefficient was solved by Bell and Marcus [11] to impose the divergence-free constraint for variable-density flows-see also [12,13].…”

Section: Scheme In Non-conservative Form: Advscmentioning

confidence: 99%

“…Subsequently, it seems that this approach was used in all the previous studies dealing with low-Mach number flows [1][2][3][4][5][6][7][8]. The approach involving a Poisson equation with variable coefficient as in Subsections 3.1 and 3.2 was preferred in [11][12][13].…”

Section: Scheme With Approximate Poisson Equation: Divsc ρmentioning

confidence: 99%

Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Nicoud¹

2000

Journal of Computational Physics

164

149

View full text Add to dashboard Cite

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“…The operator used in [5] used pressure defined on nodes. Lai [18] introduced a cell-centered approximate projection where pressure is defined at cell centers and which uses a standard five-point centereddifference stencil for the Laplacian. The D and G used in this report are those from [18]; a new L that also operates on cell-centered values will be defined by the FMM-PS solver.…”

Section: Projection Methodsmentioning

confidence: 99%

“…Because the approximate projection operators are second-order accurate approximations to an exact projection, the methods that result from each choice of V are all second-order accurate for smooth problems, but not identical. The implications of these choices are discussed and analyzed in [4] for the nodal approximate projection operator [5] and the cell-centered operator [18]. For the purposes of this paper we consider versions (1) and (2) as above.…”

Section: Projection Methodsmentioning

confidence: 99%

On Using a Fast Multipole Method-based Poisson Solver in anApproximate Projection Method

Williams¹,

Almgren²,

Puckett³

2006

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Approximate projection methods are useful computational tools for solving the equations of timedependent incompressible flow. In this report we will present a new discretization of the approximate projection in an approximate projection method. The discretizations of divergence and gradient will be identical to those in existing approximate projection methodology using cell-centered values of pressure; however, we will replace inversion of the five-point cell-centered discretization of the Laplacian operator by a Fast Multipole Method-based Poisson Solver (FMM-PS).We will show that the FMM-PS solver can be an accurate and robust component of an approximation projection method for constant density, inviscid, incompressible flow problems. Computational examples exhibiting second-order accuracy for smooth problems will be shown. The FMM-PS solver will be found to be more robust than inversion of the standard five-point cell-centered discretization of the Laplacian for certain time-dependent problems that challenge the robustness of the approximate projection methodology.

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“…The determination of other variables is then trivial by application of observation (iii). For example, from (20),…”

Section: Hyperbolic Analysismentioning

confidence: 99%

A higher-order upwind method for viscoelastic flow

Nonaka

Trebotich

Miller

et al. 2009

CAMCoS

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We present a conservative finite difference method designed to capture elastic wave propagation in viscoelastic fluids in two dimensions. We model the incompressible Navier-Stokes equations with an extra viscoelastic stress described by the Oldroyd-B constitutive equations. The equations are cast into a hybrid conservation form which is amenable to the use of a second-order Godunov method for the hyperbolic part of the equations, including a new exact Riemann solver. A numerical stress splitting technique provides a well-posed discretization for the entire range of Newtonian and elastic fluids. Incompressibility is enforced through a projection method and a partitioning of variables that suppresses compressive waves. Irregular geometry is treated with an embedded boundary/volume-of-fluid approach. The method is stable for time steps governed by the advective CourantFriedrichs-Lewy (CFL) condition. We present second-order convergence results in L 1 for a range of Oldroyd-B fluids.

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A projection method for combustion in the zero Mach number limit

Cited by 47 publications

References 8 publications

Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

On Using a Fast Multipole Method-based Poisson Solver in anApproximate Projection Method

A higher-order upwind method for viscoelastic flow

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