| OCR Text |
Show 47 Implementing the finite-difference approximations to the wave equation involves the evaluation of each of the nine equations 2.5 through 2.13 at the corresponding staggered grid locations identified on Section 2.3, respectively, and then substituting the fourth-order finite-difference approximations to the spatial derivatives and second-order approximations to the temporal derivatives. The resulting equations which are used in the program are shown below. P 82u(i,j,k,n) p [ ( .. k I) 2 (" . k ) (" . k I)) 8 2 = - 2 u z, J, , n + . - u z, J, , n + u z, J, , n-t ~t = 8 9 h [rxx(i + I/2,j,k)- Txx(i -I/2,j,k)) - 2~h [rxx(i + 3/2,j, k)- Txx(i- 3/2,j, k)] + 8~1 [rxy(i,j + I/2, k)- Txy(i,j- I/2, k)) - 2~h [rxy(i,j + 3/2, k)- Txy(i,j- 3/2, k)] + 8~1 [Tzx(i,j, k + I/2)- Tzx(i,j, k- I/2)) 1 - 24 h [Tzx(i,j, k + 3/2)- Tzx(i,j, k- 3/2)) 82v(i+I/2,j+1/2,k,n) p . P 82 =-2 [v(z+I/2,j+I/2,k,n+I)-2v(i+1/2,j+1/2,k,n) t ~t +v(i + I/2,j + I/2, k, n- 1)] = 8~1 [ryy{i + 1/2,j + 1, k)- Tyy(i + I/2,j, k)] 1 - 24 h [ryy(i + 1/2, j + 2, k)- Tyy(i + 1/2, j- 1, k)] 9 + 8 h [rxy(i + I, j + 1/2, k)- Txy(i, j + I/2, k)) 1 - 24 h [rxy(i + 2,j + 1/2, k)- Txy(i- 1,j + 1/2, k)] + ~1 [rzy(i + 1/2, j + 1/2, k + 1/2) -Tzy(i + 1/2,j + 1/2, k- 1/2)] (A .1) |
