NESC0847 DISPL-1.
DISPL-1, 2nd Order Nonlinear Partial Differential Equation System Solution for Kinetics Diffusion Problems
NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES
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| Program name | Package id | Status | Status date |
|---|---|---|---|
| DISPL-1 | NESC0847/01 | Tested | 16-FEB-1982 |
Machines used:
| Package ID | Orig. computer | Test computer |
|---|---|---|
| NESC0847/01 | IBM 3033 | IBM 3033 |
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3. DESCRIPTION OF PROBLEM OR FUNCTION
DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- ot two- dimensional with rectangular Cartesian, cylindrical, or shperical (in one dimension only) geometry.
DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- ot two- dimensional with rectangular Cartesian, cylindrical, or shperical (in one dimension only) geometry.
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4. METHOD OF SOLUTION
The numerical method is based on the use of Galerkin's procedure combined with the use of B-splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592.
The numerical method is based on the use of Galerkin's procedure combined with the use of B-splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM
The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code.
The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code.
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6. TYPICAL RUNNING TIME
The IBM version required 90 CPU seconds for compilation of the DISPL1 source and 100 CPU seconds for compilation and execution of the sample problems, including the plot creation jobs, on an IBM3033. The CDC version required a total of 66 CP seconds for all compilations and executions on a CDC7600 and 184 CP seconds on a CDC6600.
The following execution times were required by NEA-DB to execute the test cases on IBM 3033:
MORTRAN preprocessing of the source program: 30 CP seconds;
Test case 1 execution: 34 CP seconds;
Test case 2 execution: 5 CP seconds.
The IBM version required 90 CPU seconds for compilation of the DISPL1 source and 100 CPU seconds for compilation and execution of the sample problems, including the plot creation jobs, on an IBM3033. The CDC version required a total of 66 CP seconds for all compilations and executions on a CDC7600 and 184 CP seconds on a CDC6600.
The following execution times were required by NEA-DB to execute the test cases on IBM 3033:
MORTRAN preprocessing of the source program: 30 CP seconds;
Test case 1 execution: 34 CP seconds;
Test case 2 execution: 5 CP seconds.
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7. UNUSUAL FEATURES OF THE PROGRAM
Mixed-type systems can be treated (e.g. a parabolic-elliptic system consisting of a parabolic equation coupled with an elliptic equation). General orthogonal coordinate systems can also be treated with an appropriate choice of coefficients. Spatial domains can be heterogeneous with specified physical materials in each subdomain. Continuity or gap interface conditions can be specified. Boundary conditions can be nonlinear and can be of different types for each species and side. They need not be imposed on all sides for all species so that a class of problems larger than parabolic systems can be treated. All user- specified functions (coefficients) of the PDE system can depend on time, position, species concentrations, and, where appropriate, species gradients. The B-splines used in the spatial approximate can be any degree from zero through eleven, and the smoothness of the approximation can vary from zero to maximal smoothness. Moreover, the polynomial degree and smoothness can be different for each coordinate direction. The time-step integration features automatic time-step selection and integration order control to achieve specified local error control. MORTRAN2 preprocessing makes it convenient to customize a compilation to the size of a problem set.
Extensive dump/restart capabilities permit the user to produce intermediate results at specified times. In addition, a dump will automatically occur when the computation time is about to expire. Restarts from these dumps are invoked through input parameters. The code writes a graphics data set for use with plotting packages.
Mixed-type systems can be treated (e.g. a parabolic-elliptic system consisting of a parabolic equation coupled with an elliptic equation). General orthogonal coordinate systems can also be treated with an appropriate choice of coefficients. Spatial domains can be heterogeneous with specified physical materials in each subdomain. Continuity or gap interface conditions can be specified. Boundary conditions can be nonlinear and can be of different types for each species and side. They need not be imposed on all sides for all species so that a class of problems larger than parabolic systems can be treated. All user- specified functions (coefficients) of the PDE system can depend on time, position, species concentrations, and, where appropriate, species gradients. The B-splines used in the spatial approximate can be any degree from zero through eleven, and the smoothness of the approximation can vary from zero to maximal smoothness. Moreover, the polynomial degree and smoothness can be different for each coordinate direction. The time-step integration features automatic time-step selection and integration order control to achieve specified local error control. MORTRAN2 preprocessing makes it convenient to customize a compilation to the size of a problem set.
Extensive dump/restart capabilities permit the user to produce intermediate results at specified times. In addition, a dump will automatically occur when the computation time is about to expire. Restarts from these dumps are invoked through input parameters. The code writes a graphics data set for use with plotting packages.
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10. REFERENCES
- Carl DeBoor,
A Practical Guide to Splines, Springer-Verlag, New York, Inc.,
1978.
- A.C. Hindmarsh,
GEAR: Ordinary Differential Equation Systems Solver,
UCID-30001 Rev. 3, December 1974.
- Summary of Input Parameters for DISPL1, ANL-AMD Note, September
17, 1979.
- DISPL1, NESC No. 847.370B, DISPL1 IBM370 version Tape Description
and Implementation Information,
National Energy Software Center Note 81-41, April 22, 1981.
- DISPL1, NESC No. 847.7600B, DISPL1 CDC7600 Version Tape Descrip-
tion and Implementation Information,
National Energy Software Center Note 81-40, April 22, 1981.
- Carl DeBoor,
A Practical Guide to Splines, Springer-Verlag, New York, Inc.,
1978.
- A.C. Hindmarsh,
GEAR: Ordinary Differential Equation Systems Solver,
UCID-30001 Rev. 3, December 1974.
- Summary of Input Parameters for DISPL1, ANL-AMD Note, September
17, 1979.
- DISPL1, NESC No. 847.370B, DISPL1 IBM370 version Tape Description
and Implementation Information,
National Energy Software Center Note 81-41, April 22, 1981.
- DISPL1, NESC No. 847.7600B, DISPL1 CDC7600 Version Tape Descrip-
tion and Implementation Information,
National Energy Software Center Note 81-40, April 22, 1981.
NESC0847/01, included references:
- G.K.Leaf et al.:DISPL: A Software Package for One and Two Spatially Dimensioned
Kinetics-Diffusion Problems
ANL-77-12 Rev.1 (November 1978)
- National Energy Software Center Note 80-23
- A.James Cook and L.J.Shustek:
MORTRAN2, A Macro-Based Structured FORTRAN Extension
SLAC-PUB-1527 (January 1975)
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11. MACHINE REQUIREMENTS
The IBM version DISPL1 source requires 600K bytes of storage for compilation. Compilation and execution of the DISPL1 sample problems, including the plot creation jobs, requires a maximum of 350K bytes. The CDC version requires a maximum of 121,000 (octal) words of executable storage for the CDC7600, 140,000 (octal) words for the CDC6600, and 135,000 (octal) words for the CYBER175 execution. In the MORTRAN2 preprocessing stage, the user can easily adjust the storage requirements to the optimum for a current problem. In addition to the standard input and print files, the program requires files assigned to logical unit 10 for reading restart data, logical unit 11 for writing data for a later restart, and logical unit 12 for writing plotting data.
Main storage requirements for execution on IBM 3033 are:
MORTRAN preprocessing: 188K bytes;
test case 1: 340K bytes
test case 2: 312K bytes.
The IBM version DISPL1 source requires 600K bytes of storage for compilation. Compilation and execution of the DISPL1 sample problems, including the plot creation jobs, requires a maximum of 350K bytes. The CDC version requires a maximum of 121,000 (octal) words of executable storage for the CDC7600, 140,000 (octal) words for the CDC6600, and 135,000 (octal) words for the CYBER175 execution. In the MORTRAN2 preprocessing stage, the user can easily adjust the storage requirements to the optimum for a current problem. In addition to the standard input and print files, the program requires files assigned to logical unit 10 for reading restart data, logical unit 11 for writing data for a later restart, and logical unit 12 for writing plotting data.
Main storage requirements for execution on IBM 3033 are:
MORTRAN preprocessing: 188K bytes;
test case 1: 340K bytes
test case 2: 312K bytes.
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NESC0847/01
| File name | File description | Records |
|---|---|---|
| NESC0847_01.002 | DISPL-1 INFORMATION | 43 |
| NESC0847_01.003 | DISPL-1 SOURCE MORTRAN-2 | 7413 |
| NESC0847_01.004 | DISPL-1 MORTRAN MACROS | 233 |
| NESC0847_01.005 | MORTRAN-2 PRECOMPILER FORTRAN-4 IBM 3033 | 792 |
| NESC0847_01.006 | MORTRAN-2 MACROS | 87 |
| NESC0847_01.007 | JCL FOR MORTRAN-2 LOAD MODULE GENERATION | 40 |
| NESC0847_01.008 | DISPL-1 JCL FOR MORTRAN-2 PREPROCESSING | 13 |
| NESC0847_01.009 | DISPL-1 SOURCE FORTRAN-4 IN CARD IMAGES | 8673 |
| NESC0847_01.010 | DRIVER-1 SOURCE MORTRAN-2 FOR TEST CASE 1 | 554 |
| NESC0847_01.011 | DRIVER-1 JCL FOR MORTRAN-2 PREPROCESSING | 11 |
| NESC0847_01.012 | DRIVER-1 SOURCE FORTRAN-4 FOR TEST CASE 1 | 243 |
| NESC0847_01.013 | INPUT FOR TEST CASE 1 | 36 |
| NESC0847_01.014 | OUTPUT OF TEST CASE 1 | 467 |
| NESC0847_01.015 | JCL FOR TEST CASE 1 | 83 |
| NESC0847_01.016 | DRIVER-2 SOURCE MORTRAN2 FOR TEST CASE 2 | 658 |
| NESC0847_01.017 | DRIVER-2 JCL FOR MORTRAN-2 PREPROCESSING | 13 |
| NESC0847_01.018 | DRIVER-2 SOURCE FORTRAN-4 | 347 |
| NESC0847_01.019 | INPUT FOR TEST CASE 2 | 36 |
| NESC0847_01.020 | OUTPUT OF TEST CASE 2 | 489 |
| NESC0847_01.021 | JCL FOR TEST CASE 2 | 83 |
| NESC0847_01.022 | CONTOUR PLOT DRIVERS SOURCE (MORTRAN-2) | 615 |
| NESC0847_01.023 | CONTOUR PLOT DRIVERS SOURCE (FORTRAN-4) | 647 |
| NESC0847_01.024 | CONTOUR PLOT INPUT FOR TEST CASE | 10 |
| NESC0847_01.025 | CONTOUR BLACKBOX INPUT | 31 |
| NESC0847_01.026 | 3-D PLOT DRIVERS SOURCE (MORTRAN-2) | 689 |
| NESC0847_01.027 | 3-D PLOT DRIVERS SOURCE (FORTRAN-4) | 717 |
| NESC0847_01.028 | 3-D PLOT INPUT FOR TEST CASE | 14 |
| NESC0847_01.029 | X-SEC PLOT DRIVERS SOURCE (MORTRAN-2) | 1154 |
| NESC0847_01.030 | X-SEC PLOT DRIVERS SOURCE (FORTRAN-4) | 1105 |
| NESC0847_01.031 | X-SEC PLOT INPUT FOR TEST CASE | 13 |
| NESC0847_01.032 | DISPL-1 ORIGINAL JCL FROM NESC | 612 |
Keywords: cylindrical configuration, diffusion, fluid mechanics, heat transfer, heterogeneous effects, kinetics, nonlinear problems, numerical solution, one-dimensional, partial differential equations, space-time, spherical configuration, transients, two-dimensional.