Travelling Waves: Interplay of Low to High Reynolds Number and Tan-Cot Function Method to Solve Burger’s Equations

• 作者: Asif Ahmed Jahrul Alam Md. Kamrujjaman
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: Nonlinear PDES Tan-Cot Function Method TRAVELLING Wave Solutions Burg-er’s Equation REYNOLDS Number CRANK-NICOLSON Scheme
• 年，卷（期）: 2019,（4）
• 页码范围: 861-873
• 页数: 13页
• 分类号: O1

摘要

We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.