A method for avoiding the acoustic time step restriction in compressible flow

Kwatra, Nipun; Su, Jonathan; Gretarsson, Jon; Fedkiw, Ronald

doi:10.1016/j.jcp.2009.02.027

Cited by 131 publications

(181 citation statements)

References 17 publications

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“…Each figure also shows the resulting solution when solved using a traditional, fully explicit compressible flow solver with 3rd order accuracy in time and space, for comparison. We stress that the over-shoots near the shock front are a consequence of the semi-implicit discretization of the equations discussed in [21], as the implicit pressure system is centrally biased; to illustrate this point, we show in Figure 20: Density profile of a SOD shock tube at t = .15s, as generated by the scheme detailed in [21], using our new conservative semi-Lagrangian scheme and a CFL number of .5. We zoom in to the box [.725, .775] × [.…”

Section: Examplementioning

confidence: 99%

“…These are solved using the splitting proposed in [21]. Defining the state vector as U = (ρ, ρ u, E) T , the flux is split into its advective component, F 1 ( U ), and acoustic component F 2 ( U ):…”

Section: Compressible Flowmentioning

confidence: 99%

“…Notably the method of [21] was able to stably compute the solutions of compressible flow ignoring the CFL restriction due to the acoustic wave because of the implicit treatment of pressure in Equation (24). However, they were still limited by a CFL restriction based on the fluid velocity.…”

Section: Compressible Flowmentioning

confidence: 99%

“…was supported in part by an Intel Ph.D. Fellowship. Figure 21: Density profile of a SOD shock tube at t = .15s, as generated by the scheme detailed in [21], using our new conservative semi-Lagrangian scheme and a CFL number of 3. We zoom in to the box [.725, .775] × [.…”

Section: Acknowledgementsmentioning

confidence: 99%

“…As far as momentum and energy are concerned, we take an approach which is similar for both incompressible and compressible flows. In particular we use the method of [21] in order to solve the compressible flow equations in a way that requires an advection step followed by a pressure solve similar to incompressible flow, but which contains an identity term since pressure is based on the time dependent pressure evolution equation. Thus, both methods consist of a conservative advection step, followed by an implicit solve for the pressure, and a final pressure correction step.…”

Section: Introductionmentioning

confidence: 99%

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An unconditionally stable fully conservative semi-Lagrangian method

Lentine

Gretarsson

Fedkiw

2011

Journal of Computational Physics

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Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had.

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Section: Examplementioning

confidence: 99%

Section: Compressible Flowmentioning

confidence: 99%

Section: Compressible Flowmentioning

confidence: 99%

Section: Acknowledgementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An unconditionally stable fully conservative semi-Lagrangian method

Lentine

Gretarsson

Fedkiw

2011

Journal of Computational Physics

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Improved production implicit continuous‐fluid Eulerian method for compressible flow problems in Uintah

Tran

Berzins

2011

Numerical Methods in Fluids

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SUMMARY The implicit continuous‐fluid Eulerian (ICE) method is a successful and widely used semi‐implicit finite‐volume method that applies to flows that range from supersonic to subsonic regimes. The classical ICE method has been expanded to problems in multiphase flow, which spans a wide area of science and engineering. The ICE method is utilized by the Center for the Simulation of Accidental Fires and Explosions code Uintah written at the University of Utah to simulate explosions, fires and other fluid and fluid‐structure interaction phenomena. The ICE method used in Uintah (referred to here as Production ICE) is described in many papers by Kashiwa at Los Alamos National Laboratory and Harman at University of Utah. However, Production ICE does not perform as well as many current methods for compressible flow problems governed by the Euler equations. We show, via examples, that changing the nonconservation form of the solver in Production ICE to a conservation form improves the numerical solutions. In addition, the use of slope limiters makes it possible to suppress the nonphysical oscillations generated by the ICE method in conservation form. This new form of ICE is referred to as IMPICE, the IMproved Production ICE method. The accuracy of IMPICE for one‐dimensional Euler equations is investigated by using a number of test cases. Copyright © 2011 John Wiley & Sons, Ltd.

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Incompressible multiphase flow and encapsulation simulations using the moment‐of‐fluid method

Lian

Guo

et al. 2015

Numerical Methods in Fluids

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A moment of fluid method is presented for computing solutions to incompressible multiphase flows in which the number of materials can be greater than two. In this work, the multimaterial moment-of-fluid interface representation technique is applied to simulating surface tension effects at points where three materials meet. The advection terms are solved using a directionally split cell integrated semi-Lagrangian algorithm and the projection method is used to evaluate the pressure gradient force term. The underlying computational grid is a dynamic block structured adaptive grid. The new method is applied to multiphase problems illustrating contact line dynamics, triple junctions, and encapsulation in order to demonstrate its capabilities. Examples are given in 2D, 3D axisymmetric (R-Z), and 3D (X-Y-Z) coordinate systems.

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A method for avoiding the acoustic time step restriction in compressible flow

Cited by 131 publications

References 17 publications

An unconditionally stable fully conservative semi-Lagrangian method

An unconditionally stable fully conservative semi-Lagrangian method

Improved production implicit continuous‐fluid Eulerian method for compressible flow problems in Uintah

Incompressible multiphase flow and encapsulation simulations using the moment‐of‐fluid method

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