TY - GEN
T1 - NODAL INTEGRAL METHODS IN CURVILINEAR COORDINATES APPLIED TO QUADRILATERAL ELEMENTS
AU - Jarrah, Ibrahim
AU - Rizwan-Uddin,
N1 - Publisher Copyright:
Copyright © 2021 AMERICAN NUCLEAR SOCIETY, INCORPORATED, LA GRANGE PARK, ILLINOIS 60526.All rights reserved.
PY - 2021
Y1 - 2021
N2 - In this paper, the applicability of Nodal Integral Methods (NIM) is extended from the traditional Cartesian system to general curvilinear coordinates in 2D. The developed scheme is used to solve the convection-diffusion equation in domains discretized by quadrilateral elements. The quadrilateral elements in the Cartesian system are mapped to square elements in curvilinear coordinates using bi-linear Lagrangian interpolation functions. The governing partial differential equation, transverse-integration operator, and continuity conditions at the common edge of two nodes are derived in curvilinear coordinates. Two numerical test cases are solved to test the accuracy and the efficiency of the new method. The results show that the developed scheme is second-order accurate for all Péclet number values, even for highly distorted domains.
AB - In this paper, the applicability of Nodal Integral Methods (NIM) is extended from the traditional Cartesian system to general curvilinear coordinates in 2D. The developed scheme is used to solve the convection-diffusion equation in domains discretized by quadrilateral elements. The quadrilateral elements in the Cartesian system are mapped to square elements in curvilinear coordinates using bi-linear Lagrangian interpolation functions. The governing partial differential equation, transverse-integration operator, and continuity conditions at the common edge of two nodes are derived in curvilinear coordinates. Two numerical test cases are solved to test the accuracy and the efficiency of the new method. The results show that the developed scheme is second-order accurate for all Péclet number values, even for highly distorted domains.
KW - Arbitrary Geometry
KW - Convection-Diffusion
KW - Curvilinear Coordinates
KW - Nodal Integral Methods
KW - Quadrilateral
UR - https://www.scopus.com/pages/publications/85183598958
U2 - 10.13182/M&C21-33901
DO - 10.13182/M&C21-33901
M3 - Conference contribution
AN - SCOPUS:85183598958
T3 - Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021
SP - 2304
EP - 2313
BT - Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021
PB - American Nuclear Society
T2 - 2021 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021
Y2 - 3 October 2021 through 7 October 2021
ER -