AerE 546 % Lecture 15
Recall 2-surface method. Grid lines are curved; can
use finite diff or finite vol. Former here; will be
lectures on latter, but FYI. Actually, grid is a set of
points organized into cells.
Equations on curvilinear grids: “metric” tensor
A. Computational and physical space
Grid is not in x-y direction:
·
·
·
x,y
Grid generation produces [x(i,j),y(i,j)]. Now use that to solve equations. Map from
computational to physical. Think of i,j as a grid in ξ - η space. For example
δf/δξ = (f(i+1,j)-f(i-1,j))/(ξ(i+1,j)-ξ(i-1,j)) = (f(i+1,j)-f(i-1,j))/2
Data values of f are stored at i,j, so they are defined in computational space.
Need mapping from physical to computational; but only local (differential geometry;
hence term `metricʼ is used).
This study source was downloaded by 100000899610689 from CourseHero.com on 09-06-2025 01:28:44 GMT -05:00
1
https://www.coursehero.com/file/33324013/Lecture15pdf/
Recall 2-surface method. Grid lines are curved; can
use finite diff or finite vol. Former here; will be
lectures on latter, but FYI. Actually, grid is a set of
points organized into cells.
Equations on curvilinear grids: “metric” tensor
A. Computational and physical space
Grid is not in x-y direction:
·
·
·
x,y
Grid generation produces [x(i,j),y(i,j)]. Now use that to solve equations. Map from
computational to physical. Think of i,j as a grid in ξ - η space. For example
δf/δξ = (f(i+1,j)-f(i-1,j))/(ξ(i+1,j)-ξ(i-1,j)) = (f(i+1,j)-f(i-1,j))/2
Data values of f are stored at i,j, so they are defined in computational space.
Need mapping from physical to computational; but only local (differential geometry;
hence term `metricʼ is used).
This study source was downloaded by 100000899610689 from CourseHero.com on 09-06-2025 01:28:44 GMT -05:00
1
https://www.coursehero.com/file/33324013/Lecture15pdf/
