Numerical solution of the unsteady NavierStokes equation
Abstract
The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most firstorder accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly secondorder approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.
 Publication:

California Univ., Los Angeles Report
 Pub Date:
 December 1985
 Bibcode:
 1985ucla.reptR....O
 Keywords:

 Accuracy;
 Conservation Laws;
 Hyperbolic Functions;
 Nonoscillatory Action;
 Tvd Schemes;
 Approximation;
 Boundary Value Problems;
 Discrete Functions;
 Errors;
 Extremum Values;
 Shock Loads;
 Fluid Mechanics and Heat Transfer