期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2001
卷号：98
期号：25
页码：14198-14201
DOI：10.1073/pnas.251420998
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Hyperbolic conservation laws are foundational for many branches of continuum physics. Discontinuities in the solutions of these partial differential equations are widely recognized as a primary difficulty for numerical simulation, especially for thermal and shear discontinuities and fluid-fluid internal boundaries. We propose numerical algorithms that will (i) track these discontinuities as sharp internal boundaries, (ii) fully conserve the conserved quantities at a discrete level, even at the discontinuities, and (iii) display one order of numerical accuracy higher globally (at the discontinuity) than algorithms in common use. A significant improvement in simulation capabilities is anticipated through use of the proposed algorithms.
