Two space–time methods for solving Burgers' equation. (1st December 2021)

• Record Type: Journal Article
• Authors: Cao, Yanhua; Li, Nan; Zhang, Zitong; Fan, Zizhu
• Is Part Of: Engineering analysis with boundary elements. Volume 133(2021)
• Page Start: 248
• Page End: 254
• Publication Date: 2021-12-01
• Subjects: O241.8; 35k55 -- 65M99; Burgers' equation -- Space–time method -- Polynomial particular solutions; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.09.003
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: Burgers' equation is a kind of quasi-linear important partial differential equation appeared in many fields. The nonlinear term contained in this equation results in difficulty in finding its high precision numerical solution. Most existed research focused on one-dimensional and two-dimensional Burgers' systems. Seldom research studied the three-dimensional Burgers' problem. In this paper, two space–time methods based on the polynomial particular solutions (ST-MPPS) and the polynomial used as basis functions directly, have been proposed to solve three-dimensional Burgers' equation at different final time with different Reynolds numbers. The numerical examples show that the greatest attraction of the ST-MPPS is its high precision and robustness. When using the space–time polynomial functions method, some interesting phenomenon appears with the Reynolds number increasing.