ACCURATE DETERMINISTIC PROJECTION METHODS FOR STIFF DETONATION WAVES

Chertock, Alina1; Chu, Shaoshuai2,3; Kurganov, Alexander4,5

2024

COMMUNICATIONS IN MATHEMATICAL SCIENCES   影响因子和分区

1539-6746

We study numerical approximations of the reactive Euler equations of gas dynamics. In addition to shock, contact and rarefaction waves, these equations admit detonation waves appearing at the interface between different fractions of the reacting species. It is well-known that in order to resolve the reaction zone numerically, one has to take both space and time stepsizes to be proportional to the reaction time, which may cause the numerical method to become very computationally expensive or even impractical when the reaction is fast. Therefore, it is necessary to develop underresolved numerical methods, which are capable of accurately predicting locations of the detonation waves without resolving their detailed structure. One can distinguish between two different degrees of stiffness. In the stiff case, the reaction time is very small, while in the extremely stiff case, the reaction is assumed to occur instantaneously. In [A. KURGANOV, in Hyperbolic problems: theory, numerics, applications, Springer, Berlin, 2003], we proposed a simple underresolved method-an accurate deterministic projection (ADP) method-for one-dimensional hyperbolic systems with stiff source terms including the reactive Euler equations in the extremely stiff regime. In this paper, we extend the ADP method to the (non-extremely) stiff case, multispecies detonation models, and the two-dimensional reactive Euler equations in all of the aforementioned regimes. We also investigate ways to distinguish between different regimes in practice as well as study the limitations of the proposed ADP methods with respect to the ignition temperature. We demonstrate the accuracy and robustness of the ADP methods in a number of numerical experiments with both relatively low and large ignition temperature, and illustrate the difficulties one may face when the ignition temperature is low.

Stiff detonation waves reactive Euler equations splitting method deterministic projection method central-upwind scheme multispecies detonation

SCI

英语

其他

Mathematics

Mathematics, Applied

WOS:001292716600001

INT PRESS BOSTON, INC

Web of Science

1.North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
3.Southern Univ Sci & Technol, Shenzhen Int Ctr Math, Shenzhen 518055, Peoples R China
4.Southern Univ Sci & Technol, Shenzhen Int Ctr Math, Dept Math, Shenzhen 518055, Peoples R China
5.Southern Univ Sci & Technol, Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen 518055, Peoples R China

Chertock, Alina,Chu, Shaoshuai,Kurganov, Alexander. ACCURATE DETERMINISTIC PROJECTION METHODS FOR STIFF DETONATION WAVES[J]. COMMUNICATIONS IN MATHEMATICAL SCIENCES,2024,22(4).

Chertock, Alina,Chu, Shaoshuai,&Kurganov, Alexander.(2024).ACCURATE DETERMINISTIC PROJECTION METHODS FOR STIFF DETONATION WAVES.COMMUNICATIONS IN MATHEMATICAL SCIENCES,22(4).

Chertock, Alina,et al."ACCURATE DETERMINISTIC PROJECTION METHODS FOR STIFF DETONATION WAVES".COMMUNICATIONS IN MATHEMATICAL SCIENCES 22.4(2024).