A space-time backward substitution method for three-dimensional advection-diffusion equations

2021 ◽  
Vol 97 ◽  
pp. 77-85
Author(s):  
HongGuang Sun ◽  
Yi Xu ◽  
Ji Lin ◽  
Yuhui Zhang
Keyword(s):  
Three Dimensional ◽  
Space Time ◽  
Diffusion Equations ◽  
Substitution Method ◽  
Advection Diffusion

Analytical solutions of the space–time fractional Telegraph and advection–diffusion equations

2018 ◽  
Vol 491 ◽  
pp. 810-819 ◽  
Author(s):  
Ashraf M. Tawfik ◽  
Horst Fichtner ◽  
Reinhard Schlickeiser ◽  
A. Elhanbaly
Keyword(s):  
Analytical Solutions ◽  
Space Time ◽  
Diffusion Equations ◽  
Advection Diffusion

scholarly journals Vertex-Based Compatible Discrete Operator Schemes on Polyhedral Meshes for Advection-Diffusion Equations

2016 ◽  
Vol 16 (2) ◽  
pp. 187-212 ◽  
Author(s):  
Pierre Cantin ◽  
Alexandre Ern
Keyword(s):  
Differential Operators ◽  
Convergence Rates ◽  
Three Dimensional ◽  
Dirichlet Boundary Conditions ◽  
Diffusion Equations ◽  
Polyhedral Meshes ◽  
Advection Diffusion ◽  
Discrete Operators ◽  
Boundary Operators ◽  
Primal And Dual

AbstractWe devise and analyze vertex-based, Péclet-robust, lowest-order schemes for advection-diffusion equations that support polyhedral meshes. The schemes are formulated using Compatible Discrete Operators (CDO), namely, primal and dual discrete differential operators, a discrete contraction operator for advection, and a discrete Hodge operator for diffusion. Moreover, discrete boundary operators are devised to weakly enforce Dirichlet boundary conditions. The analysis sheds new light on the theory of Friedrichs' operators at the purely algebraic level. Moreover, an extension of the stability analysis hinging on inf-sup conditions is presented to incorporate divergence-free velocity fields under some assumptions. Error bounds and convergence rates for smooth solutions are derived and numerical results are presented on three-dimensional polyhedral meshes.

A HYBRID FINITE-ANALYTIC ALGORITHM FOR SOLVING THREE-DIMENSIONAL ADVECTION-DIFFUSION EQUATIONS

2004 ◽  
Vol 01 (03) ◽  
pp. 407-430 ◽  
Author(s):  
H. M. HU ◽  
K.-H. WANG
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Diffusion Equations ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
The Stability

The hybrid finite-analytic (HFA) method for discretization of a three-dimensional advection-diffusion equation is developed using the superposition of the HFA solutions of locally linearized one-dimensional advection-diffusion equations. An example calculation of a system of three-dimensional nonlinear equations is conducted to test the convergence and accuracy of the 7-point numerical scheme. Good agreements between calculated and analytical solutions are obtained. An algorithm based on the HFA method with multigrid technique and Gauss-Seidel iteration is also developed to solve the three-dimensional Navier-Stokes equations in a staggered grid system. The stability and efficiency of the method are demonstrated by performing calculations of the fluid flow in a three-dimensional cubic cavity with a moving top wall. The proposed procedure is observed to exhibit good rates of smoothing and almost grid-independent convergence rates in comparison with a single-grid iteration method. The results are in excellent agreement with other published computational results.

Sign in / Sign up

Export Citation Format

Share Document