An accuracy and stability study of the 2D spectral volume method

Abeele, Kris Van Den; Lacor, Christian

doi:10.1016/j.jcp.2007.05.004

Cited by 59 publications

(53 citation statements)

References 21 publications

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“…12) In fact, the cutting pattern for p2 partitions is not trivial and several partitions have been introduced. In chronological order, Liu et al 5) proposed the partition shown in Fig.…”

Section: Basic Frameworkmentioning

confidence: 99%

“…In the case of k-exact FVM, communicating all data involving a high-order wide stencil across the inter-domain boundary will be complicated and can worsen parallel efficiency. In prior works, 4,6,11) the SV method was developed for the Euler and Navier-Stokes (NS) equations in 2D, and linear stability analysis was investigated by Van den Aveele et al 12) In our previous study, 13) a 3rd-order SV scheme for the compressible Euler equations was developed and used to obtain accurate flowfield around complex commercial aircraft configurations while deploying high-lift devices. Later, an implicit SV method was developed using a nonlinear LU-SGS scheme for solving the 3D NS equations.…”

Section: Introductionmentioning

confidence: 99%

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RANS Simulation using the Spectral Volume Scheme on Unstructured Tetrahedral Grids

Haga

Furudate

Sawada

2014

AEROSPACE TECHNOLOGY JAPAN

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A high-order aerodynamics simulation code for the Reynolds-averaged Navier-Stokes (RANS) equations is developed using the spectral volume (SV) method for unstructured tetrahedral meshes. A nonlinear LU-SGS implicit scheme is used to enhance convergence to the steady state solution, and a novel reconstruction limiter for the SV method is developed to improve the accuracy and the convergence property for flows with shock waves. The turbulent viscosity is modeled by the Spalart-Allmaras (SA) one-equation model. The developed code is validated for turbulent flow over a flat plate and assessed for a transonic flowfield over a wing studied in the third AIAA drag prediction workshop (DPW-3). Computations of a turbulent flow over high-lift devices are performed, and the ability to predict complicated flowfields is demonstrated favorably via comparison with the reference data. The developed code is fully parallelized for application to large-scale industrial problems by using domain decomposition and MPI.

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“…12) In fact, the cutting pattern for p2 partitions is not trivial and several partitions have been introduced. In chronological order, Liu et al 5) proposed the partition shown in Fig.…”

Section: Basic Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

RANS Simulation using the Spectral Volume Scheme on Unstructured Tetrahedral Grids

Haga

Furudate

Sawada

2014

AEROSPACE TECHNOLOGY JAPAN

View full text Add to dashboard Cite

show abstract

“…Moreover, the polynomial base functions for the linear, quadratic and cubic reconstructions are listed in Table 1. For more details regarding partition quality and stability analysis the interested reader is referred to [16,20].…”

Section: Numerical Formulation a General Formulationmentioning

confidence: 99%

“…The ghost-creation process and edgebased data structure is the same as for the linear reconstruction case. The partition used in the present work follows the orientations given in [20] and it is shown in Fig. 1b.…”

Section: Quadratic Reconstructionmentioning

confidence: 99%

“…As a matter of fact, the same algorithm used to perform these tasks can be applied to higher-order reconstructions. The partition used in this work is the improved cubic partition [20], presented in Fig. 1c, and it has a total of 21 points, 30 edges (12 external and 18 internal edges), and 60 quadrature points The shape functions, in the sense of Eq.…”

Section: Cubic Reconstructionmentioning

confidence: 99%

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Implicit High-Order Spectral Finite Volume Method for Inviscid Compressible Flows

et al. 2010

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The present work has the objective of demonstrating the capabilities of a spectral finite volume scheme implemented in a cell-centered finite volume context for unstructured meshes. The two-dimensional Euler equations are considered to represent the flows of interest. The spatial discretization scheme is developed to achieve high resolution for flow problems governed by hyperbolic conservation laws. Roe's flux difference splitting method is used as the numerical approximate Riemann solver. Several applications are performed in order to assess the method capability compared to data available in the literature and also compared to an weighted essentially nonoscillatory scheme. There is good agreement with the comparison data, and efficiency improvements over the weighted essentially nonoscillatory method are observed. The features of the present methodology include an implicit timemarching algorithm; second-, third-, and fourth-order spatial resolution; exact high-order domain boundary representation; and a hierarchical moment limiter to treat flow solution discontinuities.

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Analysis of two fully discrete spectral volume schemes for hyperbolic equations

Wei,

Zou

2023

Numerical Methods Partial

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In this paper, we analyze two classes of fully discrete spectral volume schemes (SV) for solving the one‐dimensional scalar hyperbolic equation. These two schemes are constructed by using the forward Euler (EU) method or the second‐order Runge–Kutta (RK2) method in time‐discretization, and by letting a piecewise kth degree( is an arbitrary integer) polynomial satisfy the local conservation law in each control volume designed by subdividing the underlying mesh with Gauss–Legendre points (LSV) or right‐Radau points (RRSV). We prove that for the EU‐SV schemes, the weak(2) stability holds and the norm errors converge with optimal orders , provided that the CFL condition is satisfied. While for the RK2‐SV schemes, the weak(4) stability holds and the norm errors converge with optimal orders , provided that the CFL condition is satisfied. Here and are, respectively, the spacial and temporal mesh sizes and the constant is independent of and . Our theoretical findings have been justified by several numerical experiments.

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An accuracy and stability study of the 2D spectral volume method

Cited by 59 publications

References 21 publications

RANS Simulation using the Spectral Volume Scheme on Unstructured Tetrahedral Grids

RANS Simulation using the Spectral Volume Scheme on Unstructured Tetrahedral Grids

Implicit High-Order Spectral Finite Volume Method for Inviscid Compressible Flows

Analysis of two fully discrete spectral volume schemes for hyperbolic equations

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