A cartesian grid embedded boundary method for the compressible Navier–Stokes equations

Graves, Daniel; Colella, Phillip; Modiano, David; Johnson, Jeffrey; Sjögreen, Björn; Gao, Xinfeng

doi:10.2140/camcos.2013.8.99

Cited by 24 publications

(21 citation statements)

References 27 publications

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“…Avenues to explore include allowing viscosity to vary with temperature and increasing the resolution of the grid. Separation is also observed in other numerical results (albeit for very different cases), yet is always very difficult to identify in experiment.…”

Section: Resultsmentioning

confidence: 67%

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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Section: Resultsmentioning

confidence: 67%

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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“…For the compressible flow problem of the shock reflection from a wedge, we use the simulation parameters from Graves et al [14] shown in Table 3. As illustrated in Fig.…”

Section: Shock Reflection From a Wedgementioning

confidence: 99%

A dimensionally split Cartesian cut cell method for the compressible Navier–Stokes equations

Gokhale

Nikiforakis

Klein

2018

Journal of Computational Physics

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We present a dimensionally split method for computing solutions to the compressible Navier-Stokes equations on Cartesian cut cell meshes. The method is globally second order accurate in the L 1 norm, fully conservative, and allows the use of time steps determined by the regular grid spacing. We provide a description of the three-dimensional implementation of the method and evaluate its numerical performance by computing solutions to a number of test problems ranging from the nearly incompressible to the highly compressible flow regimes. All the computed results show good agreement with reference results from theory, experiment and previous numerical studies. To the best of our knowledge, this is the first presentation of a dimensionally split cut cell method for the compressible Navier-Stokes equations in the literature.

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“…The second order, finite volume, strongly conservative Schwartz, et al algorithm [31] has been used in many larger applications, including incompressible Navier Stokes with moving boundaries [26], compressible Navier Stokes [15] and a DNA-transport application [37]. We compare our algorithm to the Schwartz, et al algorithm by comparing both eigenvalue spectrums and the how many degrees of freedom are required to achieve a given degree of accuracy.…”

Section: Prior Artmentioning

confidence: 99%

“…Previous conservative algorithms for embedded boundaries compute fluxes that are second order [28,26,31,13,15,27,9]. In those algorithms, the cell-averages of φ are approximated to second order by pointwise values at the centroids of faces, and fluxes are constructed by differencing those pointwise values.…”

Section: Underlying Analysismentioning

confidence: 99%

A fourth-order Cartesian grid embedded boundary method for Poisson’s equation

Devendran

Graves

Johansen

et al. 2017

Commun. Appl. Math. Comput. Sci.

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In this paper, we present an fourth order algorithm to solve Poisson's equation in two and three dimensions. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We use a weighted least squares algorithm to solve for our stencils. We use convergence tests to demonstrate accuracy and we show the eigenvalues of the operator to demonstrate stability. We compare accuracy and performance with an established second order algorithm. We also discuss in depth strategies for retaining higher order accuracy in the presence of non-smooth geometries.

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A cartesian grid embedded boundary method for the compressible Navier–Stokes equations

Cited by 24 publications

References 27 publications

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

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

A dimensionally split Cartesian cut cell method for the compressible Navier–Stokes equations

A fourth-order Cartesian grid embedded boundary method for Poisson’s equation

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