4.7 Article

High-order implicit RBF-based differential quadrature-finite volume method on unstructured grids: Application to inviscid and viscous compressible flows

Related references

Note: Only part of the references are listed.
Review Mechanics

High-order methods for diffuse-interface models in compressible multi-medium flows: A review

V. Maltsev et al.

Summary: Diffuse interface models, despite interface smearing issues, provide an efficient and robust framework for simulating multi-species flows. Recent advancements in high-order accuracy schemes have allowed these models to solve discontinuities without introducing numerical instabilities in various numerical frameworks.

PHYSICS OF FLUIDS (2022)

Article Computer Science, Interdisciplinary Applications

An efficient high-order meshless method for advection-diffusion equations on time-varying irregular domains

Varun Shankar et al.

Summary: The study introduces a high-order radial basis function finite difference method for solving advection-diffusion equations on time-varying domains. The framework eliminates overlap parameters, enables tuning-free assembly of differentiation matrices on moving domains, and demonstrates high performance with high convergence rates.

JOURNAL OF COMPUTATIONAL PHYSICS (2021)

Article Computer Science, Interdisciplinary Applications

A high-order accurate meshless method for solution of incompressible fluid flow problems

Shantanu Shahane et al.

Summary: Meshless solution using radial basis functions (RBF) is an alternative to grid based methods, eliminating issues like grid skewness. By employing Polyharmonic splines (PHS), rapid convergence and solution to incompressible Navier-Stokes equations can be achieved.

JOURNAL OF COMPUTATIONAL PHYSICS (2021)

Article Computer Science, Interdisciplinary Applications

An efficient high-order least square-based finite difference-finite volume method for solution of compressible Navier-Stokes equations on unstructured grids

Y. Y. Liu et al.

Summary: This paper presents an efficient high-order finite volume method for solving the compressible Navier-Stokes equations on unstructured grids, utilizing a high-order polynomial based on Taylor series expansion to approximate the solution function. The method employs a least square-based finite difference scheme to approximate derivatives, and a discrete gas-kinetic flux solver to compute numerical fluxes at cell interfaces. Efficient time marching strategy and local reconstruction of solutions are used to solve ordinary differential equations with matching accuracy.

COMPUTERS & FLUIDS (2021)

Article Physics, Fluids & Plasmas

Efficient high-order radial basis-function-based differential quadrature-finite volume method for incompressible flows on unstructured grids

Y. Y. Liu et al.

Summary: This paper introduces an efficient high-order method based on radial basis functions and differential quadrature-finite volume for numerical simulation of incompressible flow on unstructured grids. The method approximates the solution within each control cell using a high-order polynomial and approximates derivatives using a mesh-free radial basis-function-based differential quadrature method. The lattice Boltzmann flux solver is applied to compute inviscid and viscous fluxes at cell interfaces simultaneously, contributing to improved computational efficiency.

PHYSICAL REVIEW E (2021)

Article Physics, Mathematical

A HWENO reconstruction based high-order compact gas-kinetic scheme on unstructured mesh

Xing Ji et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2020)

Article Computer Science, Interdisciplinary Applications

A two-stage fourth-order gas-kinetic scheme on unstructured hybrid mesh

Dongxin Pan et al.

COMPUTER PHYSICS COMMUNICATIONS (2019)

Article Engineering, Aerospace

Implicit high-order gas kinetic scheme for turbulence simulation

Guiyu Cao et al.

AEROSPACE SCIENCE AND TECHNOLOGY (2019)

Article Computer Science, Interdisciplinary Applications

On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy

Natasha Flyer et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2016)

Article Computer Science, Interdisciplinary Applications

A third-order compact gas-kinetic scheme on unstructured meshes for compressible Navier-Stokes solutions

Liang Pan et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2016)

Article Computer Science, Interdisciplinary Applications

An efficient and accurate two-stage fourth-order gas-kinetic scheme for the Euler and Navier-Stokes equations

Liang Pan et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2016)

Article Computer Science, Interdisciplinary Applications

Reordering of hybrid unstructured grids for an implicit Navier-Stokes solver based on OpenMP parallelization

Meng Cheng et al.

COMPUTERS & FLUIDS (2015)

Review Computer Science, Interdisciplinary Applications

High-order methods for computational fluid dynamics: A brief review of compact differential formulations on unstructured grids

H. T. Huynh et al.

COMPUTERS & FLUIDS (2014)

Article Mechanics

On the accuracy of high-order discretizations for underresolved turbulence simulations

Gregor J. Gassner et al.

THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS (2013)

Article Computer Science, Interdisciplinary Applications

The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids II: Extension to high order finite volume schemes

Wanai Li et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2012)

Article Mathematics, Applied

A CONSERVATIVE MESH-FREE SCHEME AND GENERALIZED FRAMEWORK FOR CONSERVATION LAWS

Edmond Kwan-Yu Chiu et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2012)

Article Mathematics, Applied

Resolution of computational aeroacoustics problems on unstructured grids with a higher-order finite volume scheme

X. Nogueira et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2010)

Article Computer Science, Interdisciplinary Applications

Numerical simulation of the viscous shock tube problem by using a high resolution monotonicity-preserving scheme

Virginie Daru et al.

COMPUTERS & FLUIDS (2009)

Article Engineering, Multidisciplinary

On the accuracy of finite volume and discontinuous Galerkin discretizations for compressible flow on unstructured grids

X. Nogueira et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2009)

Article Engineering, Multidisciplinary

Comparison of conservative and consistent approaches for the coupling of non-matching meshes

A. de Boer et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2008)

Article Engineering, Multidisciplinary

Finite volume solvers and Moving Least-Squares approximations for the compressible Navier-Stokes equations on unstructured grids

Luis Cueto-Felgueroso et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2007)

Article Computer Science, Interdisciplinary Applications

Spectral (finite) volume method for conservation laws on unstructured grids VI: Extension to viscous flow

YZ Sun et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2006)

Article Computer Science, Interdisciplinary Applications

Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows - Part I: Spatial discretization

KH Kim et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2005)

Article Engineering, Multidisciplinary

Error estimates of local multiquadric-based differential quadrature (LMQDQ) method through numerical experiments

H Ding et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2005)

Article Computer Science, Interdisciplinary Applications

A multidimensional gas-kinetic BGK scheme for hypersonic viscous flow

K Xu et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2005)

Article Computer Science, Interdisciplinary Applications

High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations

V Daru et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2004)

Article Engineering, Multidisciplinary

Solution of partial differential equations by a global radial basis function-based differential quadrature method

C Shu et al.

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS (2004)

Article Computer Science, Interdisciplinary Applications

Cures for the shock instability: Development of a shock-stable Roe scheme

SS Kim et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2003)

Article Computer Science, Interdisciplinary Applications

Grid convergence of high order methods for multiscale complex unsteady viscous compressible flows

B Sjögreen et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2003)

Article Computer Science, Interdisciplinary Applications

A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation

C Ollivier-Gooch et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2002)

Article Computer Science, Interdisciplinary Applications

Implicit time integration schemes for the unsteady compressible Navier-Stokes equations: Laminar flow

H Bijl et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2002)

Article Engineering, Aerospace

Multivariate interpolation for fluid-structure-interaction problems using radial basis functions

A Beckert et al.

AEROSPACE SCIENCE AND TECHNOLOGY (2001)

Article Computer Science, Interdisciplinary Applications

Numerical instabilities in upwind methods: Analysis and cures for the carbuncle phenomenon

M Pandolfi et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2001)

Article Computer Science, Interdisciplinary Applications

A high-resolution procedure for Euler and Navier-Stokes computations on unstructured grids

P Jawahar et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2000)