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Abstract

THE TAYLOR-GALERKIN (TG) METHOD HAS ALREADY PROVED A USEFUL TECHNIQUE FOR THE FINITE ELEMENT SOLUTION OF TRANSIENT PROBLEMS GOVERNED BY HYPERBOLE EQUATIONS. AFTER A BRIEF REVIEW OF THE BASIC CONCEPTS UNDERLYING THE METHOD, THE PRESENT PAPER INTRODUCES SOME RECENT ADDITIONAL DEVELOPMENTS IN THE SOLUTION OF MULTIDIMENSIONAL AND NONLINEAR PROBLEMS. A TWO-STEP VERSION OF THE ORIGINAL THIRD-ORDER ACCURATE LAX-WENDROFF TG SCHEME IS INTRODUCED FOR THE CASE OF THE LINEAR ADVECTION EQUATION IN ONE DIMENSION. IN TWO SPACE DIMENSIONS, THE TWO-STEP SCHEME DOES POSSESS A NEARLY ISOTROPIC DOMAIN OF NUMERICAL STABILITY AND THIS REPRESENTS A SIGNIFICANT ADVANTAGE WITH RESPECT TO THE ORIGINAL SINGLE STEP METHOD. THOUGH BEING DISSIPATIVE, SECOND-AND THIRD-ORDER METHODS OF LAX-WENDROFF TYPE ENCOUNTER DIFFICULTIES IN THE COMPUTATION OF WEAK SOLUTIONS OF NON-LINEAR HYPERBOLIC PROBLEMS. THESE METHODS TYPICALLY SUFFER FROM DISPERSIVE RIPPLES IN THE COMPUTED SOLUTIONS, PARTICULARLY NEAR STEEP GRADIENTS. METHODS OF LOWER ACCURACY, OR SCHEMES WITH LOCALLY ADDED ZERO-ORDER DIFFUSION, PRODUCE NO RIPPLES, BUT TEND TO SUFFER FROM EXCESSIVE NUMERICAL DIFFUSION. VARIOUS TECHNIQUES (ARTIFICAL VISCOSITY, TVD, FCT) WERE INVESTIGATED, WITHIN THE FRAMEWORK OF THE TG METHOD, IN AN ATTEMPT TO CONSTRUCT NON-OSCILLATORY SHOCK-CAPTURING SECOND-ORDER SCHEMES.

Additional information

Authors: DONEA J JRC-ISPRA SELMIN V AERITALIA, TORINO QUARTAPELLE L POLITECNICO DI MILANO, I , JRC-ISPRA;AERITALIA, TORINO;POLITECNICO DI MILANO, I
Bibliographic Reference: PAPER PRESENTED: CONFERENCE ON NUMERICAL METHODS FOR FLUID DYNAMICS, OXFORD/UK, MARCH 21-24, 1988
Availability: Can be ordered online
Record Number: 1989126215100 / Last updated on: 1989-04-01
Category: PUBLICATION
Available languages: en