A Solution Structure-Based Adaptive Approximate (SSAA) Riemann Solver for the Elastic-Perfectly Plastic Solid (Communications in Computational Physics, 2018)
The exact Riemann solver for one-dimensional elastic-perfectly plastic solidhas 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 solutionis time-consuming. In this paper, to enhance the computational efficiency of theexact 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 thesolution structure adaptively and then solving the Riemann problem with correspondingsolution structure non-iteratively can shorten the computing time and meanwhileguarantee the correctness of the final result. Numerical performance tests manifestthat the exact Riemann solver is indeed time-consuming and the ordinary approximateRiemann solver with fixed three-wave solution structure is of great error, whereas theSSAA Riemann solver is of both efficiency and accuracy. Error estimation further indicatesthat the SSAA Riemann solver has at least second-order accuracy to approachthe exact solution of the states in the star region.