Compatible Fluxes for van Leer Advection

VanderHeyden, W. B.; Kashiwa, B.A.

doi:10.1006/jcph.1998.6070

Cited by 25 publications

(14 citation statements)

References 8 publications

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“…Advect Fluids: For the fluid phase, use a suitable advection scheme, such as that described in [18], to transport mass, momentum, internal energy and specific volume. As this last item is an intensive quantity, it is converted to material volume for advection, and then reconstituted as specific volume for use in the subsequent timestep's equilibrium pressure calculation.…”

Section: Materials Stressesmentioning

confidence: 99%

An Eulerian–Lagrangian approach for simulating explosions of energetic devices

Guilkey

Harman

Banerjee

2007

Computers & Structures

109

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An approach for the simulation of explosions of "energetic devices" is described. In this context, an energetic device is a metal container filled with a high explosive (HE). Examples include bombs, mines, rocket motors or containers used in storage and transport of HE material. Explosions may occur due to detonation or deflagration of the HE material, with initiation resulting from either mechanical or thermal insult. This approach is applicable to a wide range of fluid-structure interaction scenarios, the application to energetic devices is chosen because it demonstrates the full capability of this methodology.Simulations of this type are characterized by a number of interesting and challenging behaviors. These include the transformation of the solid HE into highly pressurized gaseous products that initially occupy regions which formerly contained only solid material. This rapid pressurization of the container leads to large deformations at high strain rates and its eventual case rupture. Once the container breaks apart, the highly pressurized product gas that escapes the failing container generates shock waves that propagate through the initially quiescent surrounding fluid.The approach, which uses a finite-volume, multi-material compressible CFD formulation, within which solid materials are represented using a particle method known as the Material Point Method, is described, including certain of the sub-grid models required to close the governing equations. Results are first presented for "rate stick" and "cylinder test" scenarios, each of which involves detonating unconfined and confined HE material, respectively. Experimental data are available for these configurations and as such they serve as validation tests. Finally, results from an unvalidated "fast cook-off" simulation in which the HE is initiated by thermal input, which leads to a deflagration type of reaction, are shown.

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Section: Materials Stressesmentioning

confidence: 99%

An Eulerian–Lagrangian approach for simulating explosions of energetic devices

Guilkey

Harman

Banerjee

2007

Computers & Structures

109

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“…Although this lack of compatibility is also a discretization error, it is of a different type than the errors referred to in (c) above and is much less frequently discussed in the literature. Specific methods attempting to preserve compatibility are presented in Schär and Smolarkiewicz [4] and in VanderHeyden and Kashiwa [5], for example.…”

Section: Introductionmentioning

confidence: 99%

“…The two types of equations may be related to each other by means of Reynolds' transport theorem [6]. Equations (4) and (5) indicate that the mass and the total tracer of a Lagrangian volume are conserved along trajectories. They may therefore be used to solve for the time evolution of ρ and T .…”

Section: Introductionmentioning

confidence: 99%

Incremental Remapping as a Transport/Advection Algorithm

Dukowicz¹,

Baumgardner²

2000

Journal of Computational Physics

165

110

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“…Such a requirement is essential for robustness. However, except for a partially successful attempt by VanderHeyden and Kashiwa [10] for a restricted setting of the fraction problem, we do not have knowledge of any thoroughly satisfactory solution. The present contribution demonstrates that the component-wise limitation (1.13) can be actually replaced by a more general framework…”

Section: Introductionmentioning

confidence: 99%

Second-order slope limiters for the simultaneous linear advection of (not so) independent variables

Tran¹

2008

Communications in Mathematical Sciences

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Abstract. We propose a strategy to perform second-order enhancement using slope-limiters for the simultaneous linear advection of several scalar variables. Our strategy ensures a discrete min-max principle not only for each variable but also for any number of non-trivial combinations of them, which represent control variables. This problem arises in fluid mechanics codes using the Arbitrary Lagrange-Euler formalism, where the additional monotonicity property on control variables is required by physical considerations within the remap step.

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Compatible Fluxes for van Leer Advection

Cited by 25 publications

References 8 publications

An Eulerian–Lagrangian approach for simulating explosions of energetic devices

An Eulerian–Lagrangian approach for simulating explosions of energetic devices

Incremental Remapping as a Transport/Advection Algorithm

Second-order slope limiters for the simultaneous linear advection of (not so) independent variables

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