A second-order ADI difference scheme based on non-uniform meshes for the three-dimensional nonlocal evolution problem

2021 ◽  
Vol 102 ◽  
pp. 137-145
Author(s):  
Leijie Qiao ◽  
Wenlin Qiu ◽  
Da Xu
Keyword(s):  
Difference Scheme ◽  
Three Dimensional ◽  
Second Order ◽  
Evolution Problem

scholarly journals Algebraic Construction of a Strongly Consistent, Permutationally Symmetric and Conservative Difference Scheme for 3D Steady Stokes Flow

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 269 ◽  
Author(s):  
Xiaojing Zhang ◽  
Vladimir Gerdt ◽  
Yury Blinkov
Keyword(s):  
Difference Scheme ◽  
Stokes Flow ◽  
Stokes Equations ◽  
Integrability Condition ◽  
Three Dimensional ◽  
Algebraic Approach ◽  
Second Order ◽  
Algebraic Construction ◽  
Pressure Poisson Equation ◽  
Strongly Consistent

By using symbolic algebraic computation, we construct a strongly-consistent second-order finite difference scheme for steady three-dimensional Stokes flow and a Cartesian solution grid. The scheme has the second order of accuracy and incorporates the pressure Poisson equation. This equation is the integrability condition for the discrete momentum and continuity equations. Our algebraic approach to the construction of difference schemes suggested by the second and the third authors combines the finite volume method, numerical integration, and difference elimination. We make use of the techniques of the differential and difference Janet/Gröbner bases for performing related computations. To prove the strong consistency of the generated scheme, we use these bases to correlate the differential ideal generated by the polynomials in the Stokes equations with the difference ideal generated by the polynomials in the constructed difference scheme. As this takes place, our difference scheme is conservative and inherits permutation symmetry of the differential Stokes flow. For the obtained scheme, we compute the modified differential system and use it to analyze the scheme’s accuracy.

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