A review and comparative study of upwind biased schemes for compressible flow computation. Part I: 1 "D first" order schemes

Autores: P.R.M. Pyra, K. Morgan
Localización: Archives of computational methods in engineering: state of the art reviews, ISSN 1134-3060, Vol. 7, Nº. 1, 2000, págs. 19-55
Idioma: inglés
DOI: 10.1007/bf02736185
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Resumen
- First-order upwind biased formulations for simulating 1-D compressible flows are presented within a unified framework. A detailed study and comparison of the different formulations is important, as high-resolution extensions are known to inherit both the good and bad features of the first-order formulations used for their construction. The most popular flux difference splitting, flux vector splitting and some recently proposed hybrid splitting methodologies are considered. A finite element solution approach is adopted, as this provides a framework for the multidimensional extension of the solvers. Representative one-dimensional test cases are considered in order to provide evidence of the effectiveness and performance of the formulations. The results that are presented, together with the corresponding exact solutions, provide a set of benchmark test cases for comparison purposes