Computation of thin features over long distances using solitary waves

Steinhoff, John; Puskas, E.; Babu, Sushanth; Wenren, Yonghu; Underbill, D.

doi:10.2514/6.1997-1976

Cited by 23 publications

(8 citation statements)

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“…Such an alternative is the Vorticity Confinement (VC) method proposed by J. Steinhoff [16,17,18], designed to capture small-scale features directly on the computational grid. In the present work, we are working with the second (VC2) formulation [19,20] of the method to ensure discrete momentum conservation. The capability of VC to preserve vorticity has been verified by extensive application in the aeronautics field over the past two decades.…”

Section: Introductionmentioning

confidence: 99%

Development and analysis of high-order vorticity confinement schemes

2017

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High-order extensions of the Vorticity Confinement (VC) method are developed for the accurate computation of vortical flows, following the VC2 conservative formulation of Steinhoff. First, a high-order formulation of VC is presented for the case of the linear transport equation for decoupled schemes in space and time. A spectral analysis shows that the new nonlinear schemes have improved dispersive and dissipative properties compared to their linear counterparts at all orders of accuracy. For the Euler and Navier-Stokes equations, the original VC method is extended to 3 rd-and 5 th-order of accuracy, with the goal of developing a VC formulation that maintains the vorticity preserving capability of the original 1 st-order method and is suitable for application to high-order numerical simulations. The high-order extensions remain both independent of the choice of baseline numerical scheme and rotationally invariant since they are based on the Laplace operator. Numerical tests validate the increased order of accuracy, vorticity-preserving capability and compatibility of the VC extensions with high-order methods.

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Section: Introductionmentioning

confidence: 99%

Development and analysis of high-order vorticity confinement schemes

2017

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“…As in method (2) (Refs. [3,4]), the method uses nonlinear difference equations for computing variables at each grid node and does not involve any approximate discretization of a partial differential equation.…”

Section: Outline Of the Methodsmentioning

confidence: 99%

“…In this paper we describe the application of a new method that treats short wave equation pulses which propagate according to geometrical optics as zero-thickness surfaces on an Eulerian grid, as in Eikonal or Level Set schemes (4). However, the method automatically treats pulses that pass through each other, as in the other methods.…”

Section: Introductionmentioning

confidence: 99%

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A New Eulerian Method for the Computation of Propagating Short Acoustic and Electromagnetic Pulses

Steinhoff¹,

Fan²,

Wang³

2000

Journal of Computational Physics

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“…(A 1-D compact solution, which may span a number of grid cells, is defined in Ref [19].) Separately, we have derived a minimal possible compact solution in Ref [30]. This "subcompacton" consists of only two non zero grid points and, once formed, continues to be so for all times.…”

Section: Discretized Representation -Scalar Advectionmentioning

confidence: 99%

Simulation of high re boundary layer flows using vorticity confinement

Chitta

Steinhoff

Wenren

2014

Methods and Applications of Analysis

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Abstract. We describe how Vorticity Confinement (VC) can be regarded as a new pde formulation of the slightly viscous incompressible flow equations. These equations, when discretized and solved, generate nonlinear solitary waves that can be used to efficiently approximate a large class of external flow problems, including the effects of separating turbulent boundary layers. These problems can involve subsonic flow over complex structures such as ships, buildings, and realistic topography such as hills. These problems typically involve the simulation of a large ensemble of flow conditions for each configuration to be designed or analyzed. One of the most difficult aspects of these simulations is that often the main effects of the dynamics of thin evolving vortical structures must be solved for.The VC method appears to be effective for many of these problems, since it requires much less computing and setup time than current Navier Stokes "RANS" approximations. The method involves treating the flow over a solid body as a two-scale problem: The first component is an "outer" smoothly varying, mainly irrotational flow with perhaps large scale vortical components where standard CFD techniques can be used. The second component is composed of thin vortical regions. These vortical parts consist of mostly thin attached boundary layers, thin separating vortex sheets, which roll up and thin vortex filaments, which result from roll up. The VC method involves treating these regions with a single equation that has three equilibrium states corresponding to these regions. The equation allows transition between these equilibrium states so that for example, boundary layers can separate and roll up into vortex filaments, and vortex filaments can join and reconnect with other filaments. These properties survive discretization and require no extra logic.VC can be used to treat the entire flow in a locally-Cartesian computational grid with the solid surfaces "immersed" in the grid so that they can be quickly generated for many configurations. Adaptive or conforming fine scale grid cells are then not required to approximate the thin vortical boundary layers, or thin separating vortex sheets. Instead, vortical structures created with Vorticity Confinement, which are essentially thin, non-diffusing, or confined "Nonlinear Solitary Waves" (NSW's) are used to "carry" the vorticity in these regions. The VC method has the efficiency of panel methods, but the generality and ease of use of fixed grid Euler equation methods. In this paper we concentrate on attached and separating boundary layers; there are already in the literature a large number of papers describing the use of VC for free, convecting vortices.

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Computation of thin features over long distances using solitary waves

Cited by 23 publications

References 1 publication

Development and analysis of high-order vorticity confinement schemes

Development and analysis of high-order vorticity confinement schemes

A New Eulerian Method for the Computation of Propagating Short Acoustic and Electromagnetic Pulses

Simulation of high re boundary layer flows using vorticity confinement

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