Performance of some finite difference methods for a 3D advection–diffusion equation

Appadu, Appanah Rao; Djoko, J.K.; Gidey, H. H.

doi:10.1007/s13398-017-0414-7

Cited by 8 publications

(4 citation statements)

References 26 publications

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“…In contrast, a non-uniformly spaced quasi-variable meshes optimum, accurate implicit compact scheme determines the solution values precisely, and the same reflects in tabulated maximum absolute errors and computational orders. In Table 6, the  ∞ -errors using the proposed method at L = 20,  10 2 shows superiority over the existing method [7]. with quasi-variable meshes and uniformly spaced mesh points in Table 7, it is evident that  ∞ -norm errors and convergence order using quasi-variable mesh points high-order compact scheme is better than the uniform meshes high-order scheme.…”

Section: B < mentioning

confidence: 92%

“…Researchers may have made an excellent effort to construct a high-order scheme due to computational efficiency and reasonable accuracy [4][5][6]. In recent years, compact finite-difference discretization has been delineated for linear time-dependent convection-diffusion equations in [7][8][9][10][11]. Karaa and Othman [12] described a two-level high-resolution difference method to obtain the numerical approximations of three-dimensional ADEs with mixed derivatives.…”

Section: Introductionmentioning

confidence: 99%

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Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

Jha

Lin

2022

Research Reports on Computer Science

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A two-level implicit compact formulation with quasi-variable meshes is reported for solving three-dimensions second-order nonlinear parabolic partial differential equations. The new nineteen-point compact scheme exhibit fourth and second-order accuracy in space and time on a variable mesh steps and uniformly spaced mesh points. We have also developed an operator-splitting technique to implement the alternating direction implicit (ADI) scheme for computing the 3D advection-diffusion equation. Thomas algorithm computes each tri-diagonal matrix that arises from ADI steps in minimal computing time. The operator-splitting form is unconditionally stable. The improved accuracy is achieved at a lower cost of computation and storage because the spatial mesh parameters tune the mesh location according to solution values' behavior. The new method is successfully applied to the Navier-Stokes equation, advection-diffusion equation, and Burger's equation for the computational illustrations that corroborate the order, accuracies, and robustness of the new high-order implicit compact scheme. The main highlight of the present work lies in obtaining a fourth-order scheme on a quasi-variable mesh network, and its superiority over the comparable uniform meshes high-order compact scheme.

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Section: B < mentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

Jha

Lin

2022

Research Reports on Computer Science

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“…These techniques used in CAA to construct methods have been modified in order to optimize parameters to minimize dispersion or both dispersion and dissipation in a given scheme and the work is detailed in [17,23,[31][32][33].…”

Section: Optimization To Construct Low Dispersion Low Dissipation Schmentioning

confidence: 99%

“…Both optimization techniques dealt with minimization of the numerical dispersion [23]. An optimization technique was used on fourth-order finite difference method discretizing 3-D advection diffusion equation [33]. An optimal time step size was computed when spatial mesh size is fixed as h = 0.05.…”

Section: -D Advection-diffusion Equation Given Bymentioning

confidence: 99%

Optimized composite finite difference schemes for atmospheric flow modeling

Appadu

2019

Numerical Methods Partial

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In this paper, we use some finite difference methods in order to solve an atmospheric flow problem described by an advection-diffusion equation. This flow problem was solved by Clancy using forward-time central space (FTCS) scheme and is challenging to simulate due to large errors in phase and amplitude which are generated especially over long propagation times. Clancy also derived stability limits for FTCS scheme. We use Von Neumann stability analysis and the approach of Hindmarsch et al. which is an improved technique over that of Clancy in order to obtain the region of stability of some methods such as FTCS, Lax-Wendroff (LW), Crank-Nicolson. We also construct a nonstandard finite difference (NSFD) scheme. Properties like stability and consistency are studied. To improve the results due to significant numerical dispersion or numerical dissipation, we derive a new composite scheme consisting of three applications of LW followed by one application of NSFD. The latter acts like a filter to remove the dispersive oscillations from LW. We further improve the composite scheme by computing the optimal temporal step size at a given spatial step size using two techniques namely; by minimizing the square of dispersion error and by minimizing the sum of squares of dispersion and dissipation errors.

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The meshless Kansa method for time-fractional higher order partial differential equations with constant and variable coefficients

Haq

Hussain

2018

RACSAM

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Performance of some finite difference methods for a 3D advection–diffusion equation

Cited by 8 publications

References 26 publications

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

Optimized composite finite difference schemes for atmospheric flow modeling

The meshless Kansa method for time-fractional higher order partial differential equations with constant and variable coefficients

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