Question

Let x, y be the coordinates in the physical domain and ξ, η  be the coordinates in the computational domain. In which of these cases, the horizontal lines are stretched and the vertical lines are equally spaced?

(a) ξ=x; η=ln⁡(y+1)

(b) ξ=ln⁡(x+1); η=y

(c) ξ=x; η=y

(d) ξ=ln⁡(x+1); η=ln⁡(y+1)

Answer 1

Right answer is (a) ξ=x; η=ln⁡(y+1)

To explain: The horizontal coordinate lines are stretched means that the grids are stretched in the y-direction. Coordinates are stretched when logarithmically spaced. So, to get vertically stretched grid, η=ln⁡(y+1). Horizontal coordinates are undisturbed.