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Compact finite volume methods for the diffusion equation
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Rose, Milton E. |
| Copyright Year | 1989 |
| Description | An approach to treating initial-boundary value problems by finite volume methods is described, in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and alternating direction implicit (ADI) methods. The treatment of general curvilinear coordinates is shown to result from a specialization of these general results. |
| File Size | 1259925 |
| Page Count | 41 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19900012252 |
| Archival Resource Key | ark:/13960/t16m84z7r |
| Language | English |
| Publisher Date | 1989-09-16 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Alternating Direction Implicit Methods Boundary Value Problems Difference Equations Operators Mathematics Computational Fluid Dynamics Differential Equations Finite Volume Method Crank-nicholson Method Computational Grids Diffusion Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
