Current Developments in Mathematical Sciences

Author(s): Jianming Liu and Chaoqun Liu

DOI: 10.2174/9789811437601120020015

Hybrid Compact-WENO Scheme for the Interaction of Shock Wave and Boundary Layer

Pp: 293-311 (19)

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Abstract

SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.

Abstract

In this chapter, an introduction to hybrid Weighted Essentially non-oscillatory (WENO) method is given. The hybrid techniques including both central and compact finite difference schemes are introduced. The paper review about the driven mechanism of the high order finite scheme required for compressible flow with shock is presented. The detailed constructing processes of the compact and WENO schemes are given and the hybrid detector is introduced. Further, in particular, a series of examples in the field of the compressible flow are designed to illustrate the different methods.

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