High-Order CENO Finite-Volume Scheme with Anisotropic Adaptive Mesh Refinement: Efficient Inexact Newton Method for Steady Three-Dimensional Flows

Freret, Lucie; Ngigi, Christopher; Nguyen, Tan Tien; Sterck, Hans De; Groth, C. P. T.

doi:10.1007/s10915-022-02068-3

Cited by 3 publications

(3 citation statements)

References 55 publications

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“…A Newton iterative method is a common, robust, and efficient iterative technique for the solution of nonlinear systems of this type and is used here. The present implementation of Newton's method [20], [23], [24], make use of right-preconditioned generalized minimal residual (GMRES) iterative method [38]- [41] for solution of the linear problem. A domain-based additive Schwarz preconditioning technique is used as the global preconditioner and incomplete lowerupper factorization with fill is used as the local preconditioner to improve the convergence rate.…”

Section: Inexact Newton Methodsmentioning

confidence: 99%

“…A Godunov-type finite-volume with piecewise limited linear solution reconstruction is combined with an AMR algorithm [15], [20]- [22] permitting local refinement to obtain solutions to the governing hyperbolic system of moment equations on two-dimensional, body-fitted, multi-block grids consisting of quadrilateral cells. Time-invariant solutions of the spatially-discretized moment equations are obtained by using an inexact Newton's method combined with a preconditioned Krylov subspace iterative method [20], [23], [24]. In particular, the GMRES (Generalized Minimal RESidual) iterative method is combined with a Schwarz-type preconditioning strategy based on the multiblock grid in the iterative solution solution of linear equations at each Newton step.…”

Section: Introductionmentioning

confidence: 99%

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Efficient solution-adaptive finite-volume scheme for time-invariant multi-dimensional solutions of maximum-entropy-based 14-moment closure for non-equilibrium gases

Van Rooyen,

Groth

2023

Progress in Canadian Mechanical Engineering. Volume 6

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A computationally efficient solution-adaptive finitevolume scheme is proposed and developed for obtaining timeinvariant multi-dimensional solutions of a novel maximum-entropybased, interpolative, 14-moment closure which provides a fully hyperbolic description of non-equilibrium transport phenomena in monatomic gases, including heat transfer. Unlike the maximumentropy closure on which it is based, the interpolative closure provides approximate closed-form expressions for the closing fluxes. A Godunov-type finite-volume with piecewise limited linear solution reconstruction is combined with an adaptive mesh refinement (AMR) algorithm permitting local refinement to obtain solutions to the governing hyperbolic system of moment equations on twodimensional, body-fitted, multi-block grids consisting of quadrilateral cells. Time-invariant solutions of the spatially-discretized moment equations are obtained by using an inexact Newton's method combined with a preconditioned Krylov subspace iterative method. In particular, the GMRES (Generalized Minimal RESidual) iterative method is combined with a Schwarz-type preconditioning strategy based on the multi-block grid in the iterative solution solution of linear equations at each Newton step. The application of the 14moment closure is considered for some canonical non-equilibrium flow problems, including subsonic flow around a circular-cylinder and a lid driven cavity flow. The predictive capabilities of the 14-moment interpolative closure are shown to surpass those of the regularized Gaussian closure, which models heat transfer through the addition of elliptic terms using a regularization technique applied to the low-order Gaussian closure. The 14-moment closure is also found to predict interesting non-equilibrium phenomena, such as counter-gradient heat transfer, a highly non-equilibrium phenomenon.

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Section: Inexact Newton Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient solution-adaptive finite-volume scheme for time-invariant multi-dimensional solutions of maximum-entropy-based 14-moment closure for non-equilibrium gases

Van Rooyen,

Groth

2023

Progress in Canadian Mechanical Engineering. Volume 6

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“…Over the last several decades, significant effort has been devoted to the development of efficient computational fluid dynamics (CFD) algorithms for a variety of physically-complex flows, including the simulation of space-physics phenomena [1]- [3]. The latter are very often based on the equations of ideal magnetohydrodynamics (MHD), an extension of conventional fluid dynamic descriptions to electrically conducting fluids.…”

Section: Introductionmentioning

confidence: 99%

Variational-based data assimilation of initial value problems for ideal magnetohydrodynamic equations subject to solenoidal constraint

Arnal,

Sullivan,

Groth

2023

Progress in Canadian Mechanical Engineering. Volume 6

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Recently, the authors have proposed an adjoint-based dat assimilation strategy that optimizes initial conditions from the discrepancy of numerical solutions and observed data in computations of canonical, one-dimensional (1D), MHD problems. However, despite the success of the aforementioned study, all available information associated with the magnetic field data could not be ingested due to issues with the solenoidal property associated with the magnetic field (∇ • B = 0). Therefore, this study proposes an adjoint-based data assimilation procedure that ensures the solenoidal constraint on the magnetic field is satisfied. This new data assimilation schemes involves two novel components: (1) the initial magnetic field is expressed with a divergence-free parametrization; and (2) the ideal MHD equations are augmented with either the Powell source term or a generalized Lagrange multiplier (GLM) formulation. In the case of the former, instead of correcting the initial magnetic field directly, optimal parameters are sought so as to best match the observed data while maintaining the solenoidal property by construction. In the latter, the Powell and GLM approaches are used to remove via transport any non-zero ∇ • B errors generated within the simulation. The adjoint terms corresponding to the Powell and GLM strategies are derived and added directly to the adjoint equations of the original equation system. The proposed data assimilation schemes are assessed for 1D MHD initial value problems, and the ability to correct all components of the magnetic field is demonstrated. In addition, the extension of the data assimilation strategy to 3D simulations is discussed.

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An Evaluation of Accuracy and Efficiency of a 3D Adaptive Mesh Refinement Method with Analytical Velocity Fields

Lal

2023

Int. J. Comput. Methods

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Appropriate mesh refinement plays a vital role in the accuracy and convergence of computational fluid dynamics solvers. This work is an extension of the previous work that further demonstrates the accuracy of the 3D adaptive mesh refinement method by comparing the accuracy measures between the ones derived from the analytical fields and those identified by the refined meshes. The adaptive mesh refinement method presented in this study is based on the law of mass conservation for three-dimensional incompressible or compressible steady fluid flows. The assessment of the performance of the adaptive mesh refinement method considers its key features such as drawing closed streamline and identification of singular points, asymptotic planes, and vortex axis. Several illustrative examples of the applications of the 3D mesh refinement method with a multi-level refinement confirm the accuracy and efficiency of the proposed method. Furthermore, the results demonstrate that the adaptive mesh refinement method can provide accurate and reliable qualitative measures of 3D computational fluid dynamics problems.

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High-Order CENO Finite-Volume Scheme with Anisotropic Adaptive Mesh Refinement: Efficient Inexact Newton Method for Steady Three-Dimensional Flows

Cited by 3 publications

References 55 publications

Efficient solution-adaptive finite-volume scheme for time-invariant multi-dimensional solutions of maximum-entropy-based 14-moment closure for non-equilibrium gases

Efficient solution-adaptive finite-volume scheme for time-invariant multi-dimensional solutions of maximum-entropy-based 14-moment closure for non-equilibrium gases

Variational-based data assimilation of initial value problems for ideal magnetohydrodynamic equations subject to solenoidal constraint

An Evaluation of Accuracy and Efficiency of a 3D Adaptive Mesh Refinement Method with Analytical Velocity Fields

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