A High-Order-Accurate Unstructured Mesh Finite-Volume Scheme for the Advection–Diffusion Equation

2002 ◽  
Vol 181 (2) ◽  
pp. 729-752 ◽  
Author(s):  
Carl Ollivier-Gooch ◽  
Michael Van Altena
Keyword(s):  
Diffusion Equation ◽  
Finite Volume ◽  
Unstructured Mesh ◽  
High Order ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

A High-Order Central ENO Finite-Volume Scheme for Three-Dimensional Low-Speed Viscous Flows on Unstructured Mesh

2015 ◽  
Vol 17 (3) ◽  
pp. 615-656 ◽  
Author(s):  
Marc R. J. Charest ◽  
Clinton P. T. Groth ◽  
Pierre Q. Gauthier
Keyword(s):  
Finite Volume ◽  
Unstructured Mesh ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Unstructured Meshes ◽  
High Order ◽  
Finite Volume Scheme ◽  
Low Speed ◽  
Volume Scheme

AbstractHigh-order discretization techniques offer the potential to significantly reduce the computational costs necessary to obtain accurate predictions when compared to lower-order methods. However, efficient and universally-applicable high-order discretizations remain somewhat illusive, especially for more arbitrary unstructured meshes and for incompressible/low-speed flows. A novel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is proposed for the solution of the conservation equations of viscous, incompressible flows on three-dimensional unstructured meshes. Similar to finite element methods, coordinate transformations are used to maintain the scheme’s order of accuracy even when dealing with arbitrarily-shaped cells having non-planar faces. The proposed scheme is applied to the pseudo-compressibility formulation of the steady and unsteady Navier-Stokes equations and the resulting discretized equations are solved with a parallel implicit Newton-Krylov algorithm. For unsteady flows, a dual-time stepping approach is adopted and the resulting temporal derivatives are discretized using the family of high-order backward difference formulas (BDF). The proposed finite-volume scheme for fully unstructured mesh is demonstrated to provide both fast and accurate solutions for steady and unsteady viscous flows.

scholarly journals High-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Baojin Su ◽  
Ziwen Jiang
Keyword(s):  
Diffusion Equation ◽  
Finite Volume ◽  
High Order ◽  
Convergence Order ◽  
Finite Volume Scheme ◽  
Interpolation Operator ◽  
Step Size ◽  
Numerical Examples ◽  
Volume Scheme ◽  
The Difference

AbstractBased on an L1 interpolation operator, a new high-order compact finite volume scheme is derived for the 2D multi-term time fractional sub-diffusion equation. It is shown that the difference scheme is unconditionally convergent and stable in $L_{\infty }$ L ∞ -norm. The convergence order is $O(\tau ^{2-\alpha }+h_{1}^{4}+h_{2}^{4})$ O ( τ 2 − α + h 1 4 + h 2 4 ) , where τ is the temporal step size and $h_{1}$ h 1 is the spatial step size in one direction, $h_{2}$ h 2 is the spatial step size in another direction. Two numerical examples are implemented, testifying to their efficiency and confirming their convergence order.

scholarly journals A Compact High Order Finite Volume Scheme for Advection-Diffusion-Reaction Equations

2009 ◽  
Author(s):  
M. J. H. Anthonissen ◽  
J. H. M. ten Thije Boonkkamp ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Finite Volume ◽  
High Order ◽  
Diffusion Reaction ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Advection Diffusion ◽  
Reaction Equations ◽  
Advection Diffusion Reaction Equations
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