A conservative finite volume method for incompressible Navier–Stokes equations on locally refined nested Cartesian grids

Applied Mathematics and Computation

Antoniadis

et al. 2018

The paper presents a low-Mach number (LM) treatment technique for high-order, Finite-Volume (FV) schemes for the Euler and the compressible Navier-Stokes equations. We concentrate our efforts on the implementation of the LM treatment for the unstructured mesh framework, both in two and three spatial dimensions, and highlight the key differences compared with the method for structured grids. The main scope of the LM technique is to at least maintain the accuracy of low speed regions without introducing artefacts and hampering the global solution and stability of the numerical scheme. Two families of spatial schemes are considered within the k-exact FV framework: the Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and the Weighted Essentially Non-Oscillatory (WENO). The simulations are advanced in time with an explicit third-order Strong Stability Preserving (SSP) Runge-Kutta method. Several flow problems are considered for inviscid and turbulent flows where the obtained solutions are compared with referenced data. The associated benefits of the method are analysed in terms of overall accuracy, dissipation characteristics, order of scheme, spatial resolution and grid composition.

Section: D Taylor-green Vortexmentioning

confidence: 99%

Low-Mach number treatment for Finite-Volume schemes on unstructured meshes

Simmonds

Applied Mathematics and Computation

Antoniadis

et al. 2018

“…This test problem when employed at relative coarse-"under-resolved" meshes, reveals the dissipation and dispersion characteristics of non-linear methods at resolutions typically found in regions close to the boundary layer for larger Reynolds number wall bounded flows. It has been widely used by many researchers to assess the behaviour of various numerical schemes [3,46,[76][77][78][79][80][81][82], in the context of iLES. Furthermore there are well-documented DNS results of Brachet et al [83] to compare against and are used as a reference for this study.…”

Section: Iles Of Taylor Green Vortex Re = 1600mentioning

confidence: 99%

Stencil selection algorithms for WENO schemes on unstructured meshes

Journal of Computational Physics

2023

In this paper, a family of stencil selection algorithms is presented for WENO schemes on unstructured meshes. The associated freedom of stencil selection for unstructured meshes, in the context of WENO schemes present a plethora of various stencil selection algorithms. The particular focus of this paper is to assess the performance of various stencil selection algorithm, investigate the parameters that dictate their robustness, accuracy and computational efficiency. Ultimately, efficient and robust stencils are pursued that can provide significant savings in computational performance, while retaining the nonoscillatory character of WENO schemes. This is achieved when making the stencil selection algorithms adaptive, based on the quality of the cells for unstructured meshes, that can in turn reduce the computational cost of WENO schemes. For assessing the performance of the developed algorithms well established test problems are employed. These include the least square approximation of polynomial functions, linear advection equation of smooth functions and solid body rotation test problem. Euler and Navier-Stokes equations test problems are also pursued such as the Shu-Osher test problem, the Double Mach Reflection, the supersonic Forward Facing step, the Kelvin-Helmholtz instability, the Taylor-Green Vortex, and the flow past a transonic circular cylinder. Crown

“…The ILES of the 3D viscous Taylor-Green vortex test problem at Re = 1600 is employed, for assessing the performance of all the schemes. It is a widely used test problem for the validation of numerical methods, and in particularly at relative coarse-"under-resolved" meshes within the LES context [6,27,29,85,[106][107][108][109][110] due to the pronounced dissipation and dispersion characteristics of non-linear methods. The computational domain is defined as Ω = [0, 2π] 3 with periodic boundary conditions.…”

Section: Iles Of Taylor Green Vortex Re = 1600mentioning

confidence: 99%

Arbitrary high order central non-oscillatory schemes on mixed-element unstructured meshes

Dumbser

2021

Computers & Fluids

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.