Discontinuous Galerkin Solution of the Navier-Stokes Equations on Deformable Domains

Persson, Per‐Olof; Peraire, J.; Bonet, Javier

doi:10.2514/6.2007-513

Cited by 65 publications

(121 citation statements)

References 12 publications

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“…We first define an intermediate variable on the initial mesh as where d 1 and d 2 are the two vertical distances (measured from the cylinder center) used to define the virtual regions. The following blending function 23 is then defined to control the mesh motion:…”

Section: Mesh Movement Controlmentioning

confidence: 99%

A high‐order solver for simulating vortex‐induced vibrations using the sliding‐mesh spectral difference method and hybrid grids

Qiu

Zhang

Liang

et al. 2019

Numerical Methods in Fluids

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Summary We present a high‐order solver for simulating vortex‐induced vibrations (VIVs) at very challenging situations, for example, VIVs of a row of very closely placed objects with large relative displacements. This solver works on unstructured hybrid grids by employing the high‐order tensor‐product spectral difference method for quadrilateral grids and the Raviart‐Thomas spectral difference method for triangular grids. To deal with the challenging situations where a traditional conforming moving mesh is incapable, we split a computational domain into nonoverlapping subdomains, where each interior subdomain encloses an object and moves freely with respect to its neighbors. A nonuniform sliding‐mesh method that ensures high‐order accuracy is developed to deal with sliding interfaces between subdomains. A monolithic approach is adopted to seamlessly couple the fluid and solid vibration equations. Moreover, the solver is parallelized to further improve its efficiency on distributed‐memory computers. Through a series of numerical tests, we demonstrate that this solver is high‐order accurate for both inviscid and viscous flows and has good parallel efficiency, making it ideal for VIV studies.

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Section: Mesh Movement Controlmentioning

confidence: 99%

A high‐order solver for simulating vortex‐induced vibrations using the sliding‐mesh spectral difference method and hybrid grids

Qiu

Zhang

Liang

et al. 2019

Numerical Methods in Fluids

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“…This study employs a nonlinear mapping, a specialization of the mapping used in Persson et al [25]. This mapping is generated by perturbing a uniform Cartesian mesh using…”

Section: Mappingmentioning

confidence: 99%

A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

Gao

Owen

Guzik

2016

Numerical Methods in Fluids

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SUMMARYA fourth-order finite-volume method for solving the Navier-Stokes equations on a mapped grid with adaptive mesh refinement is proposed, implemented, and demonstrated for the prediction of unsteady compressible viscous flows. The method employs fourth-order quadrature rules for evaluating face-averaged fluxes. Our approach is freestream preserving, guaranteed by the way of computing the averages of the metric terms on the faces of cells. The standard Runge-Kutta marching method is used for time discretization. Solutions of a smooth flow are obtained in order to verify that the method is formally fourth-order accurate when applying the nonlinear viscous operators on mapped grids. Solutions of a shock tube problem are obtained to demonstrate the effectiveness of adaptive mesh refinement in resolving discontinuities. A Mach reflection problem is solved to demonstrate the mapped algorithm on a non-rectangular physical domain. The simulation is compared against experimental results. Future work will consider mapped multiblock grids for practical engineering geometries.

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“…AS shown in the numerical examples, these errors are very small. If necessary, it is actually possible to correct for this errors as described in [41], at the expense of introducing an additional equation.…”

Section: The Geometric Conservation Lawmentioning

confidence: 99%

A discontinuous Galerkin front tracking method for two-phase flows with surface tension

Nguyen¹,

Peraire²,

Khoo³

et al. 2010

Computers & Fluids

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A Discontinuous Galerkin method for solving hyperbolic systems of conservation laws involving interfaces is presented. The interfaces are represented by a collection of element boundaries and their position is updated using an arbitrary Lagrangian-Eulerian method. The motion of the interfaces and the numerical fluxes are obtained by solving a Riemann problem. As the interface is propagated, a simple and effective remeshing technique based on distance functions regenerates the grid to preserve its quality. Compared to other interface capturing techniques, the proposed approach avoids smearing of the jumps across the interface which leads to an improvement in accuracy.Numerical results are presented for several typical two-dimensional interface problems, including flows with surface tension.

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Discontinuous Galerkin Solution of the Navier-Stokes Equations on Deformable Domains

Cited by 65 publications

References 12 publications

A high‐order solver for simulating vortex‐induced vibrations using the sliding‐mesh spectral difference method and hybrid grids

A high‐order solver for simulating vortex‐induced vibrations using the sliding‐mesh spectral difference method and hybrid grids

A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

A discontinuous Galerkin front tracking method for two-phase flows with surface tension

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