Grid Coupling in TIMCOM

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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

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.
Objective
• 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
Multi-domain examples
• From simple to complex
Multi-domain in TIMCOM
• 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
Algorithm: TAI to NPB grid
• 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
Algorithm: TAI to NPB grid
• 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 = [email protected](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

Using interpolated values in NPB
• 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
Using interpolated values in NPB
• 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
Using interpolated values in NPB
• U2(1,N,K)=U1NPB(J,K)
• U2(1,N,K) is center value
• U1NPB - Interpolated center value from TAI
• U1NPB = [email protected](I=1)
• Same for V, S and T
• No time filter due to spatial averaging
Algorithm: NPB to TAI grid
• UETAI(J,K)=U(2,(J-2)/2+127,K)
• UETAI is east face value
• U(I,J,K) from NPB
Algorithm: NPB to TAI grid
• 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
Using interpolated values in TAI
• 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
Conclusion
• 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