dc.description.abstract |
Effective and robust high resolution schemes are of vital importance for simulation of
viscous and inviscid flows. Since second-order high resolution schemes in practice are
inadquate for many applications, large efforts have been put towards developing higher-
order accurate schemes in the past. Although some progress has been made, the efforts
were frustrated by the lack of effective and robust new schemes. Therefore this thesis is
aimed at challenging this difficult but very important issue.
Some new theories and methodologies were established during this research, which covers
the linear stability analysis for high-order numerical schemes; the fully discrete techniques
for model equations; the formulation of conservative high-order schemes and the high-order
Total Variation Diminishing (TVD) schemes. According to these theories arbitrary-order
high resolution schemes can be developed. To illustrate the methodologies second-, third-,
fourth-, and 20th-order schemes are presented. These high resolution schemes were tested
and validated by solving some popular test problems for one and two dimensional Euler
and incompressible Navier-Stokes equations. The efficiency and robustness are the features
of these high-order schemes. |
en_UK |