Fast boundary-domain integral method for unsteady convection-diffusion equation with variable diffusivity using the modified Helmholtz fundamental solution

2019 ◽  
Vol 82 (4) ◽  
pp. 1441-1466 ◽  
Author(s):  
Jure Ravnik ◽  
Jan Tibuat
Keyword(s):  
Fundamental Solution ◽  
Diffusion Equation ◽  
Integral Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Variable Diffusivity ◽  
Domain Integral

Improving the Efficiency of the Nodal Integral Method With the Portable, Extensible Toolkit for Scientific Computation

2002 ◽  
Author(s):  
Allen J. Toreja ◽  
Rizwan-Uddin
Keyword(s):  
Diffusion Equation ◽  
Peclet Number ◽  
Integral Method ◽  
Time Dependent ◽  
Scientific Computation ◽  
Péclet Number ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Nodal Integral Method ◽  
Successive Over Relaxation

An existing implementation of the nodal integral method for the time-dependent convection-diffusion equation is modified to incorporate various PETSc (Portable, Extensible Toolkit for Scientific Computation) solver and preconditioner routines. In the modified implementation, the default iterative Gauss-Seidel solver is replaced with one of the following PETSc iterative linear solver routines: Generalized Minimal Residuals, Stabilized Biconjugate Gradients, or Transpose-Free Quasi-Minimal Residuals. For each solver, a Jacobi or a Successive Over-Relaxation preconditioner is used. Two sample problems, one with a low Peclet number and one with a high Peclet number, are solved using the new implementation. In all the cases tested, the new implementation with the PETSc solver routines outperforms the original Gauss-Seidel implementation. Moreover, the PETSc Stabilized Biconjugate Gradients routine performs the best on the two sample problems leading to CPU times that are less than half the CPU times of the original implementation.

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