First order hyperbolic approach for Anisotropic Diffusion equation

Chamarthi, Amareshwara Sainadh; Nishikawa, Hiroaki; Komurasaki, Kimiya

doi:10.1016/j.jcp.2019.06.064

Cited by 10 publications

(3 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We are of aware of this as the first author has previously used the same finite-volume schemes in [48] for the computation of linear diffusion and advection-diffusion equations. For nonlinear problems, a finite-difference scheme [49] has been used to obtain high-order accuracy.…”

Section: Example 47 Explosion Problemmentioning

confidence: 99%

High-Order Central-Upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) Algorithm

Chamarthi,

Frankel

2020

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, we present a novel hybrid nonlinear explicit-compact scheme for shockcapturing based on a boundary variation diminishing (BVD) reconstruction. In our approach, we combine a non-dissipative sixth-order central compact interpolation and a fifthorder monotonicity preserving scheme (MP5) through the BVD algorithm. For a smooth solution, the BVD reconstruction chooses the highest order possible interpolation, which is central, i.e. non-dissipative in the current approach and for the discontinuities, the algorithm selects the monotone scheme. This method provides an alternative to the existing adaptive upwind-central schemes in the literature. Several numerical examples are conducted with the present approach, which suggests that the current method is capable of resolving small scale flow features and has the same ability to capture sharp discontinuities as the MP5 scheme.

show abstract

Section: Example 47 Explosion Problemmentioning

confidence: 99%

High-Order Central-Upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) Algorithm

Chamarthi,

Frankel

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Finally, the FOHS method can improve viscous discretization as well as inviscid discretization. Due to these favorable characteristics, the hyperbolic methods have been implemented in various applications, including diffusion [5], anisotropic diffusion [6], advection-diffusion [7], Navier-Stokes (NS) equations [8], and three-dimensional compressible NS equations with proper handling of high Reynolds number boundary layer flows [8].…”

Section: Introductionmentioning

confidence: 99%

Hyperbolic Navier-Stokes with Reconstructed Discontinuous Galerkin Method

Li,

Lou

2023

Computational Fluid Dynamics - Recent Advances, New Perspectives and Applications

View full text Add to dashboard Cite

One of the crucial issues of computational fluid dynamics is how to discretize the viscous terms accurately. Recently, an attractive and viable alternative numerical method for solving the compressible Navier–Stokes equations is proposed. The first-order hyperbolic system (FOHS) with reconstructed discontinuous Galerkin (rDG) method was first proposed to solve advection–diffusion model equations and then extend to compressible Navier–Stokes equations. For the model advection–diffusion equation, the proposed method is reliable, accurate, efficient, and robust, benefiting from FOHS and rDG methods. To implement the method of compressible Navier–Stokes equations, the gradients of density, velocity, and temperature are introduced as auxiliary variables. Numerical experiments demonstrate that the developed HNS + rDG methods are able to achieve the designed order of accuracy for both primary variables and their gradients.

show abstract

“…The method was developed in the finite-volume framework for diffusion equation [31,[35][36][37][38], advection-diffusion equation [39,40] Navier-Stokes equations [41][42][43][44] , and incompressible Navier-Stokes equations [42,45]. Furthermore, the method was adapted to the high-order DG method by Mazaheri and Nishikawa [46] and Lou et al [47] for advection-diffusion equation on unstructured Grids.…”

Section: Introductionmentioning

confidence: 99%

High-order flux reconstruction method for the hyperbolic formulation of the incompressible Navier-Stokes equations on unstructured grids

Kamra,

Al-Salami,

2021

Preprint

View full text Add to dashboard Cite

A high-order Flux reconstruction implementation of the hyperbolic formulation for the incompressible Navier-Stokes equation is presented. The governing equations employ Chorin's classical artificial compressibility (AC) formulation cast in hyperbolic form. Instead of splitting the second-order conservation law into two equations, one for the solution and another for the gradient, the Navier-Stokes equation is cast into a first-order hyperbolic system of equations. Including the gradients in the AC iterative process results in a significant improvement in accuracy for the pressure, velocity, and its gradients. Furthermore, this treatment allows for taking larger time-steps since the hyperbolic formulation eliminates the restriction due to diffusion.Tests using the method of manufactured solutions show that solving the conventional form of the Navier-Stokes equation lowers the order of accuracy for gradients, while the hyperbolic method is shown to provide equal orders of

show abstract

First order hyperbolic approach for Anisotropic Diffusion equation

Cited by 10 publications

References 50 publications

High-Order Central-Upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) Algorithm

High-Order Central-Upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) Algorithm

Hyperbolic Navier-Stokes with Reconstructed Discontinuous Galerkin Method

High-order flux reconstruction method for the hyperbolic formulation of the incompressible Navier-Stokes equations on unstructured grids

Contact Info

Product

Resources

About