Claims
- 1. A method for modeling a three-dimensional system in time comprising:
providing a three-dimensional mesh, wherein the three-dimensional mesh corresponds to a system to be modeled; generating a four-dimensional mesh based from the three-dimensional mesh, wherein the fourth dimension corresponds to a time over which the system is to be modeled; and generating a solution the four-dimensional mesh.
- 2. The method of claim 1 wherein providing the three-dimensional mesh comprises providing a three-dimensional mesh that contains data corresponding to a geological structure.
- 3. The method of claim 1 wherein the four-dimensional mesh comprises a plurality of nodes and wherein the plurality of nodes have a plurality of different time values associated therewith.
- 4. The method of claim 1 wherein the three-dimensional mesh comprises a plurality of three-dimensional simplices in a an unstructured mesh.
- 5. The method of claim 1 wherein the four-dimensional mesh comprises a plurality of four-dimensional simplices in a an unstructured mesh.
- 6. The method of claim 1 wherein generating the four-dimensional mesh comprises extruding the three-dimensional mesh in a fourth dimension.
- 7. The method of claim 6 wherein extruding the three-dimensional mesh in a fourth dimension comprises:
for each three-dimensional simplex of the three-dimensional mesh,
creating a four-dimensional prism by extruding the three-dimensional simplex in the fourth dimension, and dividing the four-dimensional prism into four four-dimensional simplices.
- 8. The method of claim 7 wherein dividing the four-dimensional prism into four four-dimensional simplexes comprises identifying the nodes of the four-dimensional prism and defining subsets of the nodes of the four-dimensional prism as vertices of the four-dimensional simplices.
- 9. The method of claim 8 wherein defining subsets of the nodes of the four-dimensional prism as four-dimensional simplices comprises identifying a node number associated with each of the nodes of the four-dimensional prism, determining a bit pattern based on the node numbers, indexing into a lookup table based on the bit pattern, and reading the vertices of the four-dimensional simplices from the table.
- 10. The method of claim 1 further comprising collapsing a plurality of simplices in the four-dimensional mesh into a single simplex in the four-dimensional mesh.
- 11. The method of claim 1 further comprising adding one or more additional nodes to the four-dimensional mesh and creating a plurality of new simplices which include the one or more additional nodes.
- 12. The method of claim 1 wherein a time step corresponding to a first time represented by the four-dimensional mesh varies across a three-dimensional spatial region of the four-dimensional mesh.
- 13. The method of claim 1 wherein providing the three-dimensional mesh comprises providing a two dimensional mesh and extruding the two dimensional mesh into the three-dimensional mesh.
- 14. A computer readable medium having one or more instructions embodied therein, wherein the instructions are configured to cause a computer to:
convert a three-dimensional mesh to a four-dimensional mesh, wherein the three-dimensional mesh corresponds to a system to be modeled and the four-dimensional mesh corresponds to the system to be modeled over a range of time; and generate a solution the four-dimensional mesh.
- 15. The computer readable medium of claim 14 wherein the instructions are configured to cause the computer to read data associated with the three-dimensional mesh.
- 16. The computer readable medium of claim 14 wherein the four-dimensional mesh comprises a plurality of nodes and wherein the instructions are configured to cause the computer to associate the plurality of nodes with a plurality of different time values.
- 17. The computer readable medium of claim 14 wherein the three-dimensional mesh comprises a plurality of three-dimensional simplices in a an unstructured mesh.
- 18. The computer readable medium of claim 14 wherein the four-dimensional mesh comprises a plurality of four-dimensional simplices in a an unstructured mesh.
- 19. The computer readable medium of claim 14 wherein the instructions are configured to cause the computer to generate the four-dimensional mesh by extruding the three-dimensional mesh in a fourth dimension.
- 20. The computer readable medium of claim 6 wherein extruding the three-dimensional mesh in a fourth dimension comprises:
for each three-dimensional simplex of the three-dimensional mesh,
creating a four-dimensional prism by extruding the three-dimensional simplex in the fourth dimension, and dividing the four-dimensional prism into four four-dimensional simplices.
- 21. The computer readable medium of claim 20 wherein dividing the four-dimensional prism into four four-dimensional simplexes comprises identifying the nodes of the four-dimensional prism and defining subsets of the nodes of the four-dimensional prism as vertices of the four-dimensional simplices.
- 22. The computer readable medium of claim 21 wherein defining subsets of the nodes of the four-dimensional prism as four-dimensional simplices comprises identifying a node number associated with each of the nodes of the four-dimensional prism, determining a bit pattern based on the node numbers, indexing into a lookup table based on the bit pattern, and reading the vertices of the four-dimensional simplices from the table.
- 23. The computer readable medium of claim 14 wherein the instructions are further configured to cause the computer to collapse a plurality of simplices in the four-dimensional mesh into a single simplex in the four-dimensional mesh.
- 24. The computer readable medium of claim 14 wherein the instructions are further configured to cause the computer to add one or more additional nodes to the four-dimensional mesh and create a plurality of new simplices which include the one or more additional nodes.
- 25. The computer readable medium of claim 14 wherein a time step corresponding to a first time represented by the four-dimensional mesh varies across a three-dimensional spatial region of the four-dimensional mesh.
- 26. The computer readable medium of claim 14 wherein the instructions are configured to cause the computer to generate the three-dimensional mesh by extruding a two dimensional mesh into the three-dimensional mesh.
- 27. A method for generating a second mesh of dimension n+1 from a first mesh of dimension n, wherein each mesh includes a plurality of simplices, the method comprising:
for each n-simplex of the first mesh,
creating an (n+1)-prism by extruding the simplex in the n+1th dimension, and dividing the (n+1)-prism into n+1 (n+1)-simplices.
- 28. The method of claim 27 wherein extruding the simplex in the n+1th dimension comprises duplicating the original simplex, displacing the duplicate simplex from the original simplex in the n+1th dimension, and defining an edge between each node of the original simplex and the corresponding node of the duplicate simplex.
- 29. The method of claim 27 wherein dividing the (n+1)-prism into n+1 (n+1)-simplexes comprises identifying the nodes of the (n+1)-prism and defining subsets of the nodes of the (n+1)-prism as vertices of the (n+1)-simplices.
- 30. The method of claim 29 wherein defining subsets of the nodes of the (n+1)-prism as (n+1)-simplices comprises identifying a node number associated with each of the nodes of the (n+1)-prism, determining a bit pattern based on the node numbers, indexing into a lookup table based on the bit pattern, and reading the vertices of the (n+1) simplices from the table.
- 31. A computer readable medium having one or more instructions embodied therein, wherein the instructions are configured to cause a computer to:
generate a second mesh of dimension n+1 from a first mesh of dimension n, wherein each mesh includes a plurality of simplices, and wherein for each n-simplex of the first mesh,
an (n+1)-prism is created by extruding the simplex in the n+1th dimension, and the (n+1)-prism is divided into n+1 (n+1)-simplices.
- 32. The computer readable medium of claim 31 wherein extruding the simplex in the n+1th dimension comprises duplicating the original simplex, displacing the duplicate simplex from the original simplex in the n+1th dimension, and defining an edge between each node of the original simplex and the corresponding node of the duplicate simplex.
- 33. The computer readable medium of claim 31 wherein dividing the (n+1)-prism into n+1 (n+1)-simplexes comprises identifying the nodes of the (n+1)-prism and defining subsets of the nodes of the (n+1)-prism as vertices of the (n+1)-simplices.
- 34. The computer readable medium of claim 33 wherein defining subsets of the nodes of the (n+1)-prism as (n+1)-simplices comprises identifying a node number associated with each of the nodes of the (n+1)-prism, determining a bit pattern based on the node numbers, indexing into a lookup table based on the bit pattern, and reading the vertices of the (n+1) simplices from the table.
RELATED APPLICATIONS
[0001] This application claims priority under 35 U.S.C. § 119(e) to U.S. Patent Application No. 60/215,697 entitled “Method and System for Oil Reservoir Simulation and Modeling” by Stephen R. Kennon, Kok Thye Lim, Scott A. Canaan, Steven B. Ward, Stuart W. Pond, Jr. and Edward J. Barragy, filed Jun. 29, 2000, which is incorporated by reference as if set forth in its entirety herein.
Provisional Applications (1)
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Number |
Date |
Country |
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60215697 |
Jun 2000 |
US |