A comparison of hyperbolic solvers for ideal and real gas flows

Abstract

Classical and recent numerical schemes for solving hyperbolic conservation laws were analyzed for computational efficiency and application to nonideal gas flows. The Roe-Pike approximate Riemann solver with entropy correction, the Harten second-order scheme and the extension of the Roe-Pike method to secondorder by the MUSCL strategy were compared for one-dimensional flows of an ideal gas. These methods require the so-called Roe's average state, which is frequently difficult and sometimes impossible to obtain. Other methods that do not require the average state are best suited for complex equations of state. Of these, the VFRoe, AUSM+ and Hybrid Lax-Friedrich-Lax-Wendroff methods were compared for one-dimensional compressible flows of a Van der Waals gas. All methods were evaluated regarding their accuracy for given mesh sizes and their computational cost for a given solution accuracy. It was shown that, even though they require more floating points and indirect addressing operations per time step, for a given time interval for integration the second-order methods are less-time consuming than the first-order methods for a required accuracy. It was also shown that AUSM+ and VFRoe are the most accurate methods and that AUSM+ is much faster than the others, and is thus recommended for nonideal one-phase gas flows.

A comparison of hyperbolic solvers II: ausm-type and Hybrid Lax-Wendroff-Lax-Friedrichs methods for two-phase flows

“…The MUSCL AUSMDV presented small oscillations only for the 10000-cell mesh. This result is particularly interesting because this behavior is different from the results for one-phase flows obtained in our previous work (Coelho et al, 2006), in which MUSCL AUSMDV was slightly better than HLFW. The MUSCL AUSM+ presented results with strong oscillatory behavior for all mesh sizes and it is not recommended.…”

“…One should bear in mind that this method has an iterative optimization of a weighting parameter, which increases accuracy but also increases the CPU time consumption. However, unlike the one-phase flow analysis, where the accuracy of the Hybrid Lax-Friedrichs-LaxWendroff method was comparable to AUSM type methods but with larger CPU time consumption (Coelho et al, 2006), this method is an alternative for Riemann solvers and AUSM type solvers with reasonable accuracy and CPU time for two-phase flows. As it does not require the jacobian matrix evaluation, it can be easily generalized for complex flow closure relations.…”

“…In our previous work (Coelho at al., 2006), a comparison was made regarding the accuracy and CPU time consumption of second-order extensions of Roe's Riemann solver, VFRoe, AUSM+ and Hybrid Lax-Friedrichs LaxWendroff for ideal and real gases modeled with cubic equations of state, including non-classical wave phenomena.…”

A Comparative Study of Flux Limiters Using New Numerical Methods in Unsteady Supersonic Flows

“…In this study, we just consider the variation of velocity, momentum, energy, etc., caused by the inertia force, so we did not ponder the external source term of the Euler equations. For the single ideal gas state, there is no capability to analyze the supersonic fluid problems suitably [4]. Therefore, in order to establish a computing method for the supersonic fluid problem, we first set up the Euler equations model considering multiple gases [3].…”

“…The numerical flux function used in this article is the AUSMDV scheme [4,12,16,17]. The ''V'' represents the ''clearage scheme of the flux vector'' in this scheme, and the ''D'' stands for the ''clearage scheme of flux difference.''…”