An Efficient Local RBF Meshless Scheme for Steady Convection–Diffusion Problems

2017 ◽  
Vol 14 (06) ◽  
pp. 1750064 ◽  
Author(s):  
Nikunja Bihari Barik ◽  
T. V. S. Sekhar
Keyword(s):  
Shape Parameter ◽  
Stable Solution ◽  
Navier Stokes ◽  
Computational Time ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Cpu Time ◽  
Numerical Studies ◽  
Steady Convection ◽  
Diffusion Problems

The efficiency of any numerical scheme measures on the accuracy of the scheme and its computational time. In this work, an efficient augmented local radial basis function finite difference (RBF-FD) scheme has been developed for steady convection–diffusion problems. The accommodative full approximation scheme–full multigrid (FAS-FMG) analogy with local refinement is adopted to achieve this efficiency. The efficiency of the method is illustrated through linear convection–diffusion equation, coupled nonlinear equation and for the incompressible Navier–Stokes (NS) equations. Numerical studies are made by using multiquadric (MQ) RBF. The upwind type nodes are considered to handle convective terms effectively for NS equations. The developed scheme saves 70–80% of the CPU time for the first two model problems and at least 50% of the CPU time for NS equations than the usual RBF-FD method found in the literature. It is found that there are optimum sets of nodes which give accurate and stable solution. It is also found that the value of the shape parameter will be lower when the number of nodes is higher. But higher the value of Re, higher will be the shape parameter.

COMPARISON BETWEEN GLOBAL, CLASSICAL DOMAIN DECOMPOSITION AND LOCAL, SINGLE AND DOUBLE COLLOCATION METHODS BASED ON RBF INTERPOLATION FOR SOLVING CONVECTION-DIFFUSION EQUATION

2008 ◽  
Vol 19 (11) ◽  
pp. 1737-1751 ◽  
Author(s):  
GAIL GUTIERREZ ◽  
WHADY FLOREZ
Keyword(s):  
Diffusion Equation ◽  
Domain Decomposition ◽  
Mixed Boundary ◽  
Domain Decomposition Method ◽  
Collocation Methods ◽  
Special Treatment ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Full Domain ◽  
Diffusion Problems

This work presents a performance comparison of several meshless RBF formulations for convection-diffusion equation with moderate-to-high Peclet number regimes. For the solution of convection-diffusion problems, several comparisons between global (full-domain) meshless RBF methods and mesh-based methods have been presented in the literature. However, in depth studies between new local RBF collocation methods and full-domain symmetric RBF collocation methods are not reported yet. The RBF formulations included: global symmetric method, symmetric double boundary collocation method, additive Schwarz domain decomposition method (DDM) when it is incorporated into two anterior approaches, and local single and double collocation methods. It can be found that the accuracy of solutions deteriorates as Pe increases, if no special treatment is used. From the numerical tests, it seems that the local methods, especially the derived double collocation technique incorporating PDE operator, are more effective than full domain approaches even with iterative DDM in solving moderate-to-high Pe convection-diffusion problems subject to mixed boundary conditions.

scholarly journals Analytical and approximate solution of two-dimensional convection-diffusion problems

2020 ◽  
Vol 10 (1) ◽  
pp. 73-77 ◽  
Author(s):  
Hatıra Günerhan
Keyword(s):  
Approximate Solution ◽  
Research Work ◽  
Convergent Series ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Transform Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Differential Transform ◽  
Diffusion Problems

In this work, we have used reduced differential transform method (RDTM) to compute an approximate solution of the Two-Dimensional Convection-Diffusion equations (TDCDE). This method provides the solution quickly in the form of a convergent series. Also, by using RDTM the approximate solution of two-dimensional convection-diffusion equation is obtained. Further, we have computed exact solution of non-homogeneous CDE by using the same method. To the best of my knowledge, the research work carried out in the present paper has not been done, and is new. Examples are provided to support our work.

Minimum Wall Distance Computations With Time-Dependent Geometry for CFD

2021 ◽  
Author(s):  
Liwu Wang ◽  
Jian Feng ◽  
Yu Liu ◽  
Sijun Zhang
Keyword(s):  
Present Method ◽  
Turbulence Models ◽  
Time Dependent ◽  
Navier Stokes ◽  
Field Function ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Wall Distance ◽  
Rans Turbulence Models ◽  
Computational Fluid Dynamics Cfd

Abstract This paper presents an efficient and scalable method to calculate the minimum wall distance (MWD), which is necessary for the Reynolds-Averaged Navier-Stokes (RANS) turbulence models. The MWD is described by the distance field function which is essentially a partial differential equation (PDE). The PDE is a type of convection-diffusion equation and can be solved by existing computational fluid dynamics (CFD) codes with minor modifications. Parallel computations for the PDE are conducted to study its efficiency and scalability. Encouraging results are obtained and demonstrate the present method is more efficient than all the alternate methods.

scholarly journals Thermal and hydrodynamic effects in the ordering of lamellar fluids

2011 ◽  
Vol 369 (1945) ◽  
pp. 2592-2599 ◽  
Author(s):  
G. Gonnella ◽  
A. Lamura ◽  
A. Tiribocchi
Keyword(s):  
High Viscosity ◽  
Navier Stokes ◽  
Finite Difference Schemes ◽  
Hydrodynamic Modes ◽  
Dynamical Equations ◽  
Navier Stokes Equation ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Low Viscosity ◽  
Hydrodynamic Effects

Phase separation in a complex fluid with lamellar order has been studied in the case of cold thermal fronts propagating diffusively from external walls. The velocity hydrodynamic modes are taken into account by coupling the convection–diffusion equation for the order parameter to a generalized Navier–Stokes equation. The dynamical equations are simulated by implementing a hybrid method based on a lattice Boltzmann algorithm coupled to finite difference schemes. Simulations show that the ordering process occurs with morphologies depending on the speed of the thermal fronts or, equivalently, on the value of the thermal conductivity ξ . At large values of ξ , as in instantaneous quenching, the system is frozen in entangled configurations at high viscosity while it consists of grains with well-ordered lamellae at low viscosity. By decreasing the value of ξ , a regime with very ordered lamellae parallel to the thermal fronts is found. At very low values of ξ the preferred orientation is perpendicular to the walls in d =2, while perpendicular order is lost moving far from the walls in d =3.

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