@Article{CiCP-25-781,
author = {Si Gao and Tiegang Liu},
title = {A Solution Structure-Based Adaptive Approximate (SSAA) Riemann Solver for the Elastic-Perfectly Plastic Solid},
journal = {Communications in Computational Physics},
year = {2018},
volume = {25},
number = {3},
pages = {781--811},
abstract = {<p style="text-align: justify;">The exact Riemann solver for one-dimensional elastic-perfectly plastic solid
has been presented in the previous work [S. Gao and T. G. Liu, Adv. Appl. Math.
Mech., 9(3), 2017, 621-650], but its iterative process of finding nonlinear equation solution
is time-consuming. In this paper, to enhance the computational efficiency of the
exact Riemann solver and provide a more practical Riemann solver for actual implementation,
we design a non-iterative solution structure-based adaptive approximate
(SSAA) Riemann solver for one-dimensional elastic-perfectly plastic solid. Judging the
solution structure adaptively and then solving the Riemann problem with corresponding
solution structure non-iteratively can shorten the computing time and meanwhile
guarantee the correctness of the final result. Numerical performance tests manifest
that the exact Riemann solver is indeed time-consuming and the ordinary approximate
Riemann solver with fixed three-wave solution structure is of great error, whereas the
SSAA Riemann solver is of both efficiency and accuracy. Error estimation further indicates
that the SSAA Riemann solver has at least second-order accuracy to approach
the exact solution of the states in the star region.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0182},
url = {http://global-sci.org/intro/article_detail/cicp/12829.html}
}