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# Grid Coupling in TIMCOM - PowerPoint PPT Presentation

Grid Coupling in TIMCOM. 鄭偉明 TAY Wee-Beng Department of Atmospheric Sciences National Taiwan University. Motivation. Multi-domain problems Problems which require 2 or more domains (grids) to solve efficiently. Arises due to difference in topography or restriction in computation resources.

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### Grid Coupling in TIMCOM

TAY Wee-Beng

Department of Atmospheric Sciences National Taiwan University

• Multi-domain problems

• Problems which require 2 or more domains (grids) to solve efficiently.

• Arises due to difference in topography or restriction in computation resources.

• To transfer values from grid A to B and vice versa efficiently and conservatively

• Efficiently

• Algorithm must not take up too much computational resources.

• Relatively simple to program.

• Conservatively

• Flux must be conserved, minimal dissipation.

• No appearance of unrealistic value.

• To ensure stability

• From simple to complex

• Features

• Both Cartesian grids (TAI and NPB)

• Same orientation, fixed in space

• NPB is twice the size of TAI

• Boundary faces of TAI positioned exactly at center of NPB cells

• UWNPB(JJ,K)= U(I3,J,K) +U(I3,J+1,K)

• UWNPB is west face value

• U(I,J,K) from TAI

• I3 = I0-3

• U2NPB(JJ,K)=0.25*[U2(I2,J,K)+ U2(I1,J,K)+

U2(I2,J+1,K)+ U2(I1,J+1,K)]

• U2NPB is center value

• U2NPB = U@(I=2)

• U2(I,J,K) from TAI

• I2 = I0-2

• Average of 4 values

• Same for V, S and T

• Same for U1NPB,

except different cell

• U(1,127,K)=IN(2,127,K)*(FLT1*UWNPB(J,K)+FLT2*U(1,127,K))

• U(1,127,K) is face value

• IN - Mask array for scalar quantities IN(I,J,K)=1,0 for water, land respectively

• UWNPB - Interpolated face value from TAI

• FLT1/2 – time filter to improve stability since TAI has finer grid, smaller time step. Use part of old value to improve stability

• TMP=U2NPB(J,K)-U1(2,N,K)

• TMP represents a small incremental difference

• Same effect as previous case to improve stability

• U2(2,N,K)=U2(2,N,K)+TMP

• U2(2,N,K) is center value

• To give a smaller and smoother increment

• Improves stability

• Same for V, S and T

• U2(1,N,K)=U1NPB(J,K)

• U2(1,N,K) is center value

• U1NPB - Interpolated center value from TAI

• U1NPB = U@(I=1)

• Same for V, S and T

• No time filter due to spatial averaging

• UETAI(J,K)=U(2,(J-2)/2+127,K)

• UETAI is east face value

• U(I,J,K) from NPB

• UI0TAI(J,K)=U2(3,(J-2)/2+127,K)

• UI0TAI is center value

• U2(I,J,K) from NPB

• Same for V, S and T

• U(I1,J,K)=IN(I1,J,K)*UETAI(J,K)

• U(I1,J,K) is face value

• IN - Mask array for scalar quantities IN(I1,J,K)=1,0 for water, land respectively

• No time filter

• U2(I0,J,K)=UI0TAI(J,K)

• U2(I0,J,K) is center value

• No time filter and IN multiplication required

• Multi-domain problems requires the use of grid coupling

• Objective to transfer values from one grid to another

• Efficient and conservative algorithm

• Use of filter to ensure smooth transition and stability