Higher-order unstructured finite volume RANS solution of turbulent compressible flows

Jalali, Alireza; Ollivier‐Gooch, Carl

doi:10.1016/j.compfluid.2016.11.004

Cited by 36 publications

(28 citation statements)

References 22 publications

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“…This work extended the idea of hp ‐adaptivity to unstructured finite volume methods. Future work will concentrate on the extension of hp ‐adaptations to our higher‐order RANS flow solver used for the solution of turbulent flows on highly anisotropic meshes over aerodynamic configurations . Moreover, we plan to extend this work to three‐dimensional problems where the problems size is considerably larger and uniform refinement is not affordable.…”

Section: Discussionmentioning

confidence: 99%

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An hp‐adaptive unstructured finite volume solver for compressible flows

Jalali

Ollivier‐Gooch

2017

Numerical Methods in Fluids

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Summary The idea of hp‐adaptation, which has originally been developed for compact schemes (such as finite element methods), suggests an adaptation scheme using a mixture of mesh refinement and order enrichment based on the smoothness of the solution to obtain an accurate solution efficiently. In this paper, we develop an hp‐adaptation framework for unstructured finite volume methods using residual‐based and adjoint‐based error indicators. For the residual‐based error indicator, we use a higher‐order discrete operator to estimate the truncation error, whereas this estimate is weighted by the solution of the discrete adjoint problem for an output of interest to form the adaptation indicator for adjoint‐based adaptations. We perform our adaptation by local subdivision of cells with nonconforming interfaces allowed and local reconstruction of higher‐order polynomials for solution approximations. We present our results for two‐dimensional compressible flow problems including subsonic inviscid, transonic inviscid, and subsonic laminar flow around the NACA 0012 airfoil and also turbulent flow over a flat plate. Our numerical results suggest the efficiency and accuracy advantages of adjoint‐based hp‐adaptations over uniform refinement and also over residual‐based adaptation for flows with and without singularities.

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Section: Discussionmentioning

confidence: 99%

“…For our computations, we use a higher‐order unstructured finite volume solver. The elements of this solver including the spatial discretization and implicit solution strategy used to obtain the steady‐state solution are described in this section briefly …”

Section: Finite Volume Flow Solvermentioning

confidence: 99%

An hp‐adaptive unstructured finite volume solver for compressible flows

Jalali

Ollivier‐Gooch

2017

Numerical Methods in Fluids

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“…For unstructured meshes, various approaches have been devised for achieving higher-order accuracy, most notably: continuous [5] and discontinuous [29] Galerkin finite element methods, the correction procedure via reconstruction formulations of the discontinuous Galerkin and spectral volume methods [31], and finite volume schemes [32]. (See the work of Andren et al [8] for a detailed comparison of numerical results).…”

Section: List Of Figuresmentioning

confidence: 99%

“…In two dimensions, unstructured high-order finite volume methods have been successfully applied to a range of aerodynamic problems: the Euler equations [27,46], laminar Navier-Stokes equations [33,40], and turbulent Reynolds Averaged Navier-Stokes (RANS) equations [32]. Although taking the effects of turbulence into consideration is necessary for correctly capturing many aerodynamic flows, threedimensional results are scarce and limited to the solution of Euler and laminar Navier-Stokes equations [25,40].…”

Section: List Of Figuresmentioning

confidence: 99%

“…This particular choice of basis functions has the advantage that the discrete solution u h will resemble the Taylor expansion of the exact solution u, which is particularly useful in theoretical analysis [54]. However, there are situations, e.g., highly anisotropic meshes, in which it would be more beneficial to use other basis functions [32]. Such a case will be introduced in Chapter 3.…”

Section: K-exact Reconstructionmentioning

confidence: 99%

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A Higher-Order Unstructured Finite Volume Solver for Three-Dimensional Compressible Flows

Hoshyari

Ollivier‐Gooch

2018

2018 AIAA Aerospace Sciences Meeting

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High-order accurate numerical discretization methods are attractive for their potential to significantly reduce the computational costs compared to the traditional second-order methods. Among the various unstructured higher-order discretization schemes, the k-exact reconstruction finite volume method is of interest for its straightforward mathematical formulation, and its compatibility with the current lowerorder industrial solvers. However, current three-dimensional finite volume solvers are limited to the solution of inviscid and laminar viscous flow problems. Since three-dimensional turbulent flows appear in many industrial applications, the current thesis takes the first step towards the development of a threedimensional higher-order finite volume solver for the solution of both inviscid and viscous turbulent steady-state flow problems.The k-exact finite volume formulation of the governing equations is rederived in a dimension-independent manner, where the negative Spalart-Allmaras turbulence model is employed. This one-equation model is reasonably accurate for many flow conditions, and its simplicity makes it a good starting point for the development of numerical algorithms. Then, the three-dimensional mesh preprocessing steps for a finite volume simulation are presented, including higher-order accurate numerical quadrature, and capturing the boundary curvature in highly anisotropic meshes. Also, the issues of k-exact reconstruction in handling highly anisotropic meshes are reviewed and addressed.Since three-dimensional problems can require much more memory than their two-dimensional counterparts, solution methods that work in two dimensions might not be feasible in three dimensions anymore.As an attempt to overcome this issue, a practical and parallel scalable method for the solution of the discretized system of nonlinear equations is presented. Finally, the solution of four three-dimensional test problems are studied: Poisson's equation in a cubic domain, inviscid flow over a sphere, turbulent flow over a flat plate, and turbulent flow over an extruded NACA 0012 airfoil. The solution is verified, and the resource consumption of the flow solver is measured.The results demonstrate the benefit and practicality of using higher-order methods for obtaining a certain level of accuracy.ii Lay SummaryThe finite volume method is a popular numerical scheme for the solution of aerodynamic flow problems.Although conventional finite volume schemes are mostly second-order accurate, there has been a growing interest in higher-order accurate numerical methods, since they can be considerably more efficient in terms of computational resources for achieving a certain level of accuracy.Higher-order finite volume methods have been successfully developed for a wide range of two-dimensional flow problems. Nevertheless, numerical methods that work in two dimensions might not be feasible in three dimensions anymore, since three-dimensional problems can require much more memory than their two-dimensional counterparts. The current th...

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A truncation error analysis of third‐order MUSCL scheme for nonlinear conservation laws

Nishikawa

2020

Numerical Methods in Fluids

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This article is a rebuttal to the claim found in the literature that the monotonic upstream‐centered scheme for conservation laws (MUSCL) cannot be third‐order accurate for nonlinear conservation laws. We provide a rigorous proof for third‐order accuracy of the MUSCL scheme based on a careful and detailed truncation error analysis. Throughout the analysis, the distinction between the cell average and the point value will be strictly made for the numerical solution as well as for the target operator. It is shown that the average of the solutions reconstructed at a face by Van Leer's κ‐scheme recovers a cubic solution exactly with κ=1/3, the same is true for the average of the nonlinear fluxes evaluated by the reconstructed solutions, and a dissipation term is already sufficiently small with a third‐order truncation error. Finally, noting that the target spatial operator is a cell‐averaged flux derivative, we prove that the leading truncation error of the MUSCL finite‐volume scheme is third‐order with κ=1/3. The importance of the diffusion scheme is also discussed: third‐order accuracy will be lost when the third‐order MUSLC scheme is used with an incompatible fourth‐order diffusion scheme for convection‐diffusion problems. Third‐order accuracy is verified by thorough numerical experiments for both steady and unsteady problems. This article is intended to serve as a reference to clarify confusions about third‐order accuracy of the MUSCL scheme, as a guide to correctly analyze and verify the MUSCL scheme for nonlinear equations, and eventually as the basis for clarifying high‐order unstructured‐grid schemes in a subsequent article.

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Higher-order unstructured finite volume RANS solution of turbulent compressible flows

Cited by 36 publications

References 22 publications

An hp‐adaptive unstructured finite volume solver for compressible flows

An hp‐adaptive unstructured finite volume solver for compressible flows

A Higher-Order Unstructured Finite Volume Solver for Three-Dimensional Compressible Flows

A truncation error analysis of third‐order MUSCL scheme for nonlinear conservation laws

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