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Compact High Order Schemes for the Euler Equations

出版	Defense Technical Information Center, 1988
URL	http://books.google.com.hk/books?id=qKNCAQAAMAAJ&hl=&source=gbs_api

註釋An implicit approximate factorization (AF) algorithm is constructed which has the following characteristics. In 2-D: The scheme is unconditionally stable, has a 3 x 3 stencil and at steady state has a fourth order spatial accuracy. The temporal evolution is time accurate either to 1st or 2nd order through choice of parameter. In 3-D: The scheme has almost the same properties as in 2-D except that it is now only conditionally stable, with the stability condition (the CFL number) being dependent on the cell aspect ratios, Delta y/Delta x and Delta z/Delta x. The stencil is still compact and fourth order accuracy at steady state is maintained. Numerical experiments on a 2-D shock-reflection problem show the expected improvement over lower order schemes, not only in accuracy (measured by the L2 error) but also in the dispersion. It is also shown how the same technique is immediately extendable to Runge Kutta type schemes resulting in improved stability in addition to the enhanced accuracy. Keywords: Euler equations; Compact schemes; High order accuracy; Dispersion.