The Geometric Conservation Law - A link between finite-difference and finite-volume methods of flow computation on moving grids

Thomas, P. D.; Lombard, C. K.

doi:10.2514/6.1978-1208

Cited by 48 publications

(24 citation statements)

References 9 publications

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“…Care must be taken to ensure that metric identities ensuring the commutative properties of partial differentials are respected. 10,11 Close to solid boundaries, differencing is performed with lower-order stencils, first with the centered 7-point DRP 1 stencil and then with classical centered and finally non-centered 5-point fourth-order stencils. A no-slip solid-wall boundary condition is applied by imposing u = v = 0 at the boundary, and also ∂p/∂n = 0 thanks to a one-sided 5-point fourth-order stencil.…”

Section: Differencing Filtering and Time Integration Techniques Boumentioning

confidence: 99%

High-order Curvilinear Simulations of Flows Around Non-Cartesian Bodies

Marsden

Bogey

Bailly

2004

10th AIAA/CEAS Aeroacoustics Conference

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The current work describes the application of high-order numerical techniques to single or multiple overset curvilinear body-fitted grids, demonstrating the feasibility of direct computations of noise radiated by flows around complex non-Cartesian bodies. Flows of both physical and industrial interest can be investigated with this approach. We first rapidly describe the numerical techniques implemented in our curvilinear simulations. The explicit high-order differencing and filtering schemes are presented, as well as their application to the curvilinear Navier-Stokes equations. We then present brief results of various 2-D acoustic simulations. First the flow around a cylinder, and the associated acoustic field, are described. The diameter-based Reynolds number Re D = 150 is under the critical Reynolds number of the onset of 3-D phenomena in the vortex-shedding. Simulation results can thus be meaningfully compared to experimental measurements. A case of acoustic scattering is then examined. A non-compact monopolar source is placed half way between two differently sized cylinders. A complex diffraction pattern is created, and resulting RMS pressure data are compared to the analytical solution. Finally the noise generated by a low Reynolds number laminar flow around a NACA 0012 airfoil is presented.

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Section: Differencing Filtering and Time Integration Techniques Boumentioning

confidence: 99%

High-order Curvilinear Simulations of Flows Around Non-Cartesian Bodies

Marsden

Bogey

Bailly

2004

10th AIAA/CEAS Aeroacoustics Conference

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“…For deforming volumes, careful treatment of this term is required, in particular, to ensure satisfaction of the geometric conservation law [26]. For a second-order treatment of the above integrations, a piecewise linear reconstruction is used to approximate the solution variables within elements.…”

Section: Numerical Approximations To Spatial Integralsmentioning

confidence: 99%

On the use of general elements in fluid dynamics simulations

Chalasani

Senguttuvan

Thompson

et al. 2007

Commun. Numer. Meth. Engng.

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SUMMARYAs flow solvers have become more sophisticated, many now have the capability to handle meshes with general polyhedral elements, i.e. general elements. In response, researchers have begun to develop mesh generation strategies that exploit nonstandard element types. General elements have been employed locally in near-body extruded meshes to improve mesh quality and have also been used in solution adaptive mesh refinement algorithms. In this paper, we present two mesh generation strategies that employ general elements. We also discuss how a specific flow solver is formulated to work with general elements. We demonstrate our approach by presenting simulation results for two realistic configurations. We close with a discussion that highlights future research directions.

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“…Spurious sources of errors are avoided by ensuring that the Geometric Conservation Law (GCL) [20] is satisfied in the discretization of the transient and advection terms:…”

Section: Mesh Deformationmentioning

confidence: 99%

“…The temporal optimization was performed on the presented MIT model with the adopted 28000 nodes and again on the faster -16.67 Hz (1000 RPM) operating frequency simulation. Resolutions of 100, 500, 1000, 2000 and 4000 timesteps/cycle are examined and the results are shown in Figure 4.6 and Figure 4.7 20 . As well as with the spatial refinement, a weak influence of the timestep size is observed on the computed values for the gas pressure.…”

Section: Temporal Discretizationmentioning

confidence: 99%

“…Definition of a dynamic physical problem, to be set before the static model in such a numerical simulation, starts with the settings of the boundary and initial conditions. 20 ANSYS CFX uses a fully implicit solver, making no tight restrictions on the maximum Courant number (Courant-Friedrichs-Lewy -CFL condition) for convergence. Nevertheless, for the reader's feel, with the varying velocities and the deforming mesh, the cycle-maximum values of the Courant number for the selected 2000 timesteps/cycle are 0.14 max RMS and 2.52 ensemble-max absolute value.…”

Section: Boundary Conditions and Initial Conditionsmentioning

confidence: 99%

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Fluid flow and heat transfer in a helium gas spring : computational fluid dynamics and experiments

Lekic¹

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The Geometric Conservation Law - A link between finite-difference and finite-volume methods of flow computation on moving grids

Cited by 48 publications

References 9 publications

High-order Curvilinear Simulations of Flows Around Non-Cartesian Bodies

High-order Curvilinear Simulations of Flows Around Non-Cartesian Bodies

On the use of general elements in fluid dynamics simulations

Fluid flow and heat transfer in a helium gas spring : computational fluid dynamics and experiments

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