Fast, Unstructured-Mesh Finite-Element Method for Nonlinear Subsonic Flow

Eller, David

doi:10.2514/1.c031738

Cited by 6 publications

(6 citation statements)

References 18 publications

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“…This gap introduces a geometrical boundary in the CFD domain. Following the method presented in [1], to support a jump in the value of the potential across the wake, finite elements are not connected across the wake surface ( Figure 2). Elements that share a node with the wake are only attached to one side of the wake, so that all wake nodes must be present at least twice.…”

Section: Standard Body-fitted Wake Methodsmentioning

confidence: 99%

“…The advantage of full-potential solvers is that only a single, scalar, partial-differential equation (conservation of mass) is needed to obtain flow solutions, instead of five coupled equations (conservation of mass, momentum, energy). Therefore, for a given mesh the number of variables is five times lower than for the solution of the Euler equations [1]. Potential solvers can reproduce flow solutions with shock waves, such as in transonic [2,3,4,5,6] and supersonic [7,8,9,10] flows.…”

Section: Mdavari E-mail: MD Civil1983@yahoocommentioning

confidence: 99%

“…In order to support the jump in the potential, Nishida and Drela [11] developed a finite element method in which elements are not connected across the wake surface. David Eller improved the method's flexibility and robustness by enforcing the pressure-equality wake-boundary condition using a least-squares approach [1,12]. However, both methods require a body-fitted mesh around the wake.…”

Section: Mdavari E-mail: MD Civil1983@yahoocommentioning

confidence: 99%

“…. " [1]. Based on this, the present paper is focused on the development of an embedded wake approach.…”

Section: Mdavari E-mail: MD Civil1983@yahoocommentioning

confidence: 99%

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A cut finite element method for the solution of the full-potential equation with an embedded wake

et al. 2018

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Potential flow solvers represent an appealing alternative for the simulation of non-viscous subsonic flows. In order to deliver accurate results, such techniques require prescribing explicitly the so called Kutta condition, as well as adding a special treatment on the "wake" of the body. The wake is traditionally modelled by introducing a gap in the CFD mesh, which requires an often laborious meshing work. The novelty of the proposed work is to embed the wake within the CFD domain. The approach has obvious advantages in the context of aeroelastic optimization, where the position of the wake may change due to evolutionary steps of the geometry. This work presents a simple, yet effective, method for the imposition of the embedded wake boundary condition. The presented method preserves the possibility of employing iterative techniques in the solution of the linear problems which stem out of the discretization. Validation and verification of the solver are performed for a NACA 0012 airfoil.

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Section: Standard Body-fitted Wake Methodsmentioning

confidence: 99%

Section: Mdavari E-mail: MD Civil1983@yahoocommentioning

confidence: 99%

Section: Mdavari E-mail: MD Civil1983@yahoocommentioning

confidence: 99%

“…. " [1]. Based on this, the present paper is focused on the development of an embedded wake approach.…”

Section: Mdavari E-mail: MD Civil1983@yahoocommentioning

confidence: 99%

See 2 more Smart Citations

A cut finite element method for the solution of the full-potential equation with an embedded wake

et al. 2018

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show abstract

“…Full-potential solvers offer an appealing tradeoff, enlarging the range of application to capture nonlinear compressibility effects while providing fast solutions. However, standard full-potential solvers require modeling a gap in the mesh, hindering their effective use for aeroelastic optimization, where the wake's position may change due to the structural response and the geometry's evolutionary steps [1,2]. To overcome this problem, an embedded wake approach for potential transonic solvers is proposed.…”

Section: Introductionmentioning

confidence: 99%

A Transonic Potential Solver with an Embedded Wake Approach using Multivalued Finite Elements

López¹,

Jones²,

Núñez³

et al. 2021

9th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

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A potential transonic solver with an embedded wake is presented. The flow outside of attached boundary layers of streamlined bodies flying at high Reynold numbers can be assumed to be irrotational and isentropic. This assumption reduces the Navier-Stokes equations to a single scalar nonlinear partial differential equation, namely the full-potential equation (FPE). The FPE expresses the conservation of mass in terms of the velocity potential. In this work, the FPE is discretized using a standard Galerkin finite element method, and the nonlinear system of equations stemming from the discretization is solved using Newton's method. An artificial compressibility method is used to stabilize the problem in supersonic flow regions. This method prevents the Jacobian from becoming singular and allows capturing shock waves. To include the viscosity effects in the lift generation, a model for the trailing wake needs to be introduced. In the presented method, the wake is modeled as a straight surface in the free-stream direction. This assumption is relaxed allowing mass flux across the wake. To capture the discontinuity in the velocity potential across the wake, a multivalued element method is employed. This implicit description of the wake within the mesh presents an effective approach to perform fluidstructure interaction computations and apply aeroelastic optimization methods, where the position of the wake changes during consecutive iterations. The solver is implemented in Kratos Multi-Physics and verified for different angles of attack and free-stream conditions. Since the pressure does not change in the transverse direction of the boundary layer, the FPE yields accurate lift, induced drag, and moment computations.

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A Parallel Dynamic Asynchronous Framework for Uncertainty Quantification by Hierarchical Monte Carlo Algorithms

et al. 2021

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The necessity of dealing with uncertainties is growing in many different fields of science and engineering. Due to the constant development of computational capabilities, current solvers must satisfy both statistical accuracy and computational efficiency. The aim of this work is to introduce an asynchronous framework for Monte Carlo and Multilevel Monte Carlo methods to achieve such a result. The proposed approach presents the same reliability of state of the art techniques, and aims at improving the computational efficiency by adding a new level of parallelism with respect to existing algorithms: between batches, where each batch owns its hierarchy and is independent from the others. Two different numerical problems are considered and solved in a supercomputer to show the behavior of the proposed approach.

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Fast, Unstructured-Mesh Finite-Element Method for Nonlinear Subsonic Flow

Cited by 6 publications

References 18 publications

A cut finite element method for the solution of the full-potential equation with an embedded wake

A cut finite element method for the solution of the full-potential equation with an embedded wake

A Transonic Potential Solver with an Embedded Wake Approach using Multivalued Finite Elements

A Parallel Dynamic Asynchronous Framework for Uncertainty Quantification by Hierarchical Monte Carlo Algorithms

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