Details
| Original language | English |
|---|---|
| Pages (from-to) | 1231-1249 |
| Number of pages | 19 |
| Journal | Engineering with computers |
| Volume | 37 |
| Issue number | 2 |
| Early online date | 28 Nov 2019 |
| Publication status | Published - Apr 2021 |
Abstract
The main aim of this paper is to present new and simple numerical methods for solving the time-dependent transport equation on the sphere in spherical coordinates. We use two techniques, namely generalized moving least squares and moving kriging least squares to find the new formulations for approximating the advection operator in spherical coordinates such that any singularities have been omitted. Another feature of the methods considered here is that they do not depend on the background mesh or triangulation for approximation, which they could be applied on the transport equation in spherical coordinates easily with different distribution points. Furthermore, due to the eigenvalue stability of the dicretized advection operator via two proposed approximations, an implicit-explicit linear multistep method has been applied to discretize the time variable. The fully discrete scheme obtained here yields a linear system of algebraic equations at each time step, which is solved via the biconjugate gradient stabilized algorithm with zero-fill incomplete lower-upper (ILU) preconditioner. Three well-known test problems, namely “solid body rotation”, “vortex roll-up” and “deformational flow” are solved to demonstrate our developments. Also for the first test problem, we apply a simple positivity-preserving filter at the end of each time step, which keeps the transported variable positive.
Keywords
- An implicit-explicit linear multistep method, Biconjugate gradient-stabilized method, Generalized moving least squares approximation, Meshless methods, Moving kriging least squares interpolation, Transport equation on the sphere
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Computer Science(all)
- Computer Science Applications
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In: Engineering with computers, Vol. 37, No. 2, 04.2021, p. 1231-1249.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Numerical investigation on the transport equation in spherical coordinates via generalized moving least squares and moving kriging least squares approximations
AU - Mohammadi, Vahid
AU - Dehghan, Mehdi
AU - Khodadadian, Amirreza
AU - Wick, Thomas
PY - 2021/4
Y1 - 2021/4
N2 - The main aim of this paper is to present new and simple numerical methods for solving the time-dependent transport equation on the sphere in spherical coordinates. We use two techniques, namely generalized moving least squares and moving kriging least squares to find the new formulations for approximating the advection operator in spherical coordinates such that any singularities have been omitted. Another feature of the methods considered here is that they do not depend on the background mesh or triangulation for approximation, which they could be applied on the transport equation in spherical coordinates easily with different distribution points. Furthermore, due to the eigenvalue stability of the dicretized advection operator via two proposed approximations, an implicit-explicit linear multistep method has been applied to discretize the time variable. The fully discrete scheme obtained here yields a linear system of algebraic equations at each time step, which is solved via the biconjugate gradient stabilized algorithm with zero-fill incomplete lower-upper (ILU) preconditioner. Three well-known test problems, namely “solid body rotation”, “vortex roll-up” and “deformational flow” are solved to demonstrate our developments. Also for the first test problem, we apply a simple positivity-preserving filter at the end of each time step, which keeps the transported variable positive.
AB - The main aim of this paper is to present new and simple numerical methods for solving the time-dependent transport equation on the sphere in spherical coordinates. We use two techniques, namely generalized moving least squares and moving kriging least squares to find the new formulations for approximating the advection operator in spherical coordinates such that any singularities have been omitted. Another feature of the methods considered here is that they do not depend on the background mesh or triangulation for approximation, which they could be applied on the transport equation in spherical coordinates easily with different distribution points. Furthermore, due to the eigenvalue stability of the dicretized advection operator via two proposed approximations, an implicit-explicit linear multistep method has been applied to discretize the time variable. The fully discrete scheme obtained here yields a linear system of algebraic equations at each time step, which is solved via the biconjugate gradient stabilized algorithm with zero-fill incomplete lower-upper (ILU) preconditioner. Three well-known test problems, namely “solid body rotation”, “vortex roll-up” and “deformational flow” are solved to demonstrate our developments. Also for the first test problem, we apply a simple positivity-preserving filter at the end of each time step, which keeps the transported variable positive.
KW - An implicit-explicit linear multistep method
KW - Biconjugate gradient-stabilized method
KW - Generalized moving least squares approximation
KW - Meshless methods
KW - Moving kriging least squares interpolation
KW - Transport equation on the sphere
UR - http://www.scopus.com/inward/record.url?scp=85075894658&partnerID=8YFLogxK
U2 - 10.1007/s00366-019-00881-3
DO - 10.1007/s00366-019-00881-3
M3 - Article
AN - SCOPUS:85075894658
VL - 37
SP - 1231
EP - 1249
JO - Engineering with computers
JF - Engineering with computers
SN - 0177-0667
IS - 2
ER -