A High-Order Moving Mesh Kinetic Scheme Based on WENO Reconstruction for Compressible Flows on Unstructured Meshes

Xu, Xihua; Ni, Guoxi; Jiang, Song

doi:10.1007/s10915-013-9705-0

Cited by 17 publications

(20 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[32,31,12]). From (25), the scalar expressions are obtained by replacing f (u) by f (u), w by ⌘, and Kij by a•nij. Concerning the ALE related aspects, following the closure proposed in [27], all the geometrical quantities needed to evaluate Ri are obtained on the mid-point averaged mesh T…”

Section: Finite Volume Discrete Approximationmentioning

confidence: 99%

“…We use in this paper the elliptic mesh deformation technique used for time dependent flows also in [44,17,45,29,25]. Given an error monitor function !, the mapping x = M (X, t) which equidistributes !…”

Section: Adaptive Mesh Deformationmentioning

confidence: 99%

“…For example, for the FV scheme, taking the limit for t ! 0, and using equations (23), (25) we obtain the one step projection over the sub…”

Section: High Order Projections From Ale Remapsmentioning

confidence: 99%

“…Particular cases of these two implementations have already been considered in literature (see e.g. [17] and [25] for the ALE). However, their impact on the overall cost of the simulation, and on the quality of the results has never been assessed.…”

Section: Adaptive Algorithmsmentioning

confidence: 99%

“…At the opposite, once the grid has been adapted, one can evolve the flow with an Arbitrary-Lagrangian-Eulerian formulation of the equations, as suggested e.g. in [25]. In this case, the properties of the flow solutions are only determined by the scheme.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

r−adaptation for Shallow Water flows: conservation, well balancedness, efficiency

Arpaia¹,

Ricchiuto²

2018

Computers & Fluids

View full text Add to dashboard Cite

We investigate the potential of the so-called "relocation" mesh adaptation in terms of resolution and e ciency for the simulation of free surface flows in the near shore region. Our work is developed in three main steps. First, we consider several Arbitrary Lagrangian Eulerian (ALE) formulations of the shallow water equations on moving grids, and provide discrete analogs in the Finite Volume and Residual Distribution framework. The compliance to all the physical constraints, often in competition, is taken into account. We consider di↵erent formulations allowing to combine volume conservation (DGCL) and equilibrium (Well-Balancedness), and we clarify the relations between the so-called pre-balanced form of the equations (Rogers et al., J.Comput.Phys. 192, 2003), and the classical upwiniding of the bathymetry term gradients (Bermudez and Vazquez, Computers and Fluids 235, 1994). Moreover, we propose a simple remap of the bathymetry based on high accurate quadrature on the moving mesh which, while preserving an accurate representation of the initial data, also allows to retain mass conservation within an arbitrary accuracy. Second, the coupling of the resulting schemes with a mesh partial di↵erential equation is studied. Since the flow solver is based on genuinely explicit time stepping, we investigate the e ciency of three coupling strategies in terms of cost overhead w.r.t. the flow solver. We analyze the role of the solution remap necessary to evaluate the error monitor controlling the adaptation, and propose simplified formulations allowing a reduction in computational cost. The resulting ALE algorithm is compared with the rezoning Eulerian approach with interpolation proposed e.g. in (Tang and Tang, SINUM 41, 2003). An alternative cost e↵ective Eulerian approach, still allowing a full decoupling between adaptation and flow evolution steps is also proposed. Finally, a thorough numerical evaluation of the methods discussed is performed. Numerical results on propagation, and inundation problems shows that the best compromise between accuracy and CPU time is provided by a full ALE formulation. If a loose coupling with the mesh adaptation is sought, then the cheaper Eulerian approach proposed is shown to provide results quite close to the ALE.

show abstract

Section: Finite Volume Discrete Approximationmentioning

confidence: 99%

Section: Adaptive Mesh Deformationmentioning

confidence: 99%

“…For example, for the FV scheme, taking the limit for t ! 0, and using equations (23), (25) we obtain the one step projection over the sub…”

Section: High Order Projections From Ale Remapsmentioning

confidence: 99%

Section: Adaptive Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

r−adaptation for Shallow Water flows: conservation, well balancedness, efficiency

Arpaia¹,

Ricchiuto²

2018

Computers & Fluids

View full text Add to dashboard Cite

show abstract

A Runge‐Kutta–based WENO reconstruction on moving mesh for compressible fluids

Niu

2019

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

In this paper, we construct a high-order moving mesh method based on total variation diminishing Runge-Kutta and weighted essential nonoscillatory reconstruction for compressible fluid system. Beginning with the integral form of fluid system, we get the semidiscrete system with an arbitrary mesh velocity. We use weighted essential nonoscillatory reconstruction to get the space accuracy on moving meshes, and the time accuracy is obtained by modified Runge-Kutta method; the mesh velocity is determined by moving mesh method. One-and two-dimensional numerical examples are presented to demonstrate the efficient and accurate performance of the scheme.

show abstract

An arbitrary Lagrangian–Eulerian discontinuous Galerkin method for two‐dimensional compressible flows on adaptive quadrilateral meshes

Zhao

Huang

et al. 2023

Numerical Methods in Fluids

View full text Add to dashboard Cite

In this article, a discontinuous Galerkin (DG) scheme on the adaptive quadrilateral meshes is proposed to simulate two‐dimensional compressible flows in the direct arbitrary Lagrangian–Eulerian (ALE) framework. In our scheme, the Euler equations are discretized in the reference element with the help of a bilinear map. A kind of Taylor expansion basis functions in the reference element is used to construct the interpolation polynomials of variables. We describe the property that the material derivatives of the basis functions used in the DG discretization are equal to zero, with which the scheme is simplified. Furthermore, the mesh velocity in our ALE framework is obtained by implementing the approach of mesh movement based on the variational principle from [Adaptive mesh methods for one‐ and two‐dimensional hyperbolic conservation laws. SIAM J Numer Anal. 2003;41:487–515]. This approach of mesh movement automatically concentrates the mesh nodes near the regions with large gradient values of the variables and can greatly improve the resolution of the solution near these regions. In addition, a WENO (weighted essentially non‐oscillatory) reconstruction helps our scheme remove the numerical oscillations. Some numerical examples are presented to demonstrate the accuracy, high resolution, and robustness of our scheme.

show abstract

A High-Order Moving Mesh Kinetic Scheme Based on WENO Reconstruction for Compressible Flows on Unstructured Meshes

Cited by 17 publications

References 32 publications

r−adaptation for Shallow Water flows: conservation, well balancedness, efficiency

r−adaptation for Shallow Water flows: conservation, well balancedness, efficiency

A Runge‐Kutta–based WENO reconstruction on moving mesh for compressible fluids

An arbitrary Lagrangian–Eulerian discontinuous Galerkin method for two‐dimensional compressible flows on adaptive quadrilateral meshes

Contact Info

Product

Resources

About