(untitled) (International journal of artificial intelligence, 2025)
The Burgers equation plays a fundamental role in the study of nonlinear gas dynamics, viscous flow, and turbulence modeling. It serves as a simplified representation of the Navier–Stokes equations, enabling the investigation of shock wave formation and dissipation phenomena. This paper presents a spectral grid-based approach for solving the Burgers equation to simulate gas flow processes. The spectral method allows for high accuracy in the spatial representation of the flow field by using global basis functions, typically Fourier or Chebyshev polynomials. The study examines the mathematical formulation of the Burgers equation, discusses its application in gas flow modeling, and demonstrates the computational efficiency and convergence characteristics of the spectral method compared to finite difference schemes. Numerical experiments illustrate the ability of the spectral solution to capture nonlinear wave propagation and viscous damping effects with minimal numerical dispersion. The findings highlight the method’s suitability for high-resolution modeling of one-dimensional and quasi-one-dimensional gas flows in engineering and physical simulations.