Longquan Yong

Nov 13, 2024 | mdpi.com | Yue Sun |Qian Chen |Tao Chen |Longquan Yong

1. IntroductionBurgers’ equation [1] is a fundamental quasi-linear partial differential equation (PDE) that appears in various fields, including gas dynamics, acoustic wave, biological process, and traffic flow modeling. It provides a simpler version of the Navier–Stokes equations, capturing the interplay between nonlinear convection and diffusion.

Aug 16, 2024 | mdpi.com | Yue Sun |Tao Chen |Longquan Yong |Qian Chen

1. IntroductionThe robust and accurate simulation of fracture propagation phenomena is of paramount importance across a wide range of applications ranging from material science to geotechnique engineering.

May 22, 2024 | mdpi.com | Yue Sun |Qian Chen |Tao Chen |Longquan Yong

1. IntroductionAs a fundamental nonlinear convection-diffusion equation, Burgers’ equation, named after Johannes M. Burgers [1], takes its form by simplifying the Navier–Stokes (N-S) equations while retaining the convection and viscosity terms. This model provides valuable insights into the behavior of complex waves occurring in turbulence, gas dynamics, nonlinear acoustics, traffic flow, etc.