Accession Number:

ADA235464

Title:

An Adaptive Mesh-Moving and Local Refinement Method for Time-Dependent Partial Differential Equations

Descriptive Note:

Corporate Author:

RENSSELAER POLYTECHNIC INST TROY NY

Personal Author(s):

• Arney, David C.
• Flaherty, Joseph E.

Report Date:

1990-03-01

Pagination or Media Count:

25.0

Abstract:

We discuss mesh-moving, static mesh regeneration, and local mesh-refinement algorithms that can be used with a finite difference or finite element scheme to solve initial boundary value problems for vector systems of time-dependent partial differential equations in two space dimensions and time. A coarse based mesh of quadrilateral cells is moved by an algebraic mesh-movement function so as to follow and isolate spatially distinct phenomena. The local mesh-refinement method recursively divides the time step and spatial cells of the moving base mesh in regions where error indicators are high until a prescribed tolerance is satisfied. The static mesh-regeneration procedure is used to create a new base mesh when the existing one becomes to distorted. The adaptive methods have been combined with a MacCormack finite difference scheme for hyperbolic systems and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples.

Descriptors:

• *DIFFERENCE EQUATIONS
• REGENERATION(ENGINEERING)
• TIME DEPENDENCE
• CELLS
• FINITE ELEMENT ANALYSIS
• MOTION
• MESH
• TIME
• FINITE DIFFERENCE THEORY
• BOUNDARY VALUE PROBLEMS
• ERRORS
• TOLERANCE
• PARTIAL DIFFERENTIAL EQUATIONS
• VECTOR ANALYSIS
• ADAPTATION
• REFINING
• STATICS
• INDICATORS
• SPATIAL DISTRIBUTION
• REPRINTS

Subject Categories:

• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE