Modeling of Supersonic Wave and Shock Propagation using the Lattice Boltzmann Method

Authors

• Timothy P. Schroeder, Embry-Riddle Aeronautical UniversityFollow

Faculty Mentor

Leitao Chen

Abstract

The lattice Boltzmann method (LBM) has emerged as a mesoscopic alternative to traditional Navier-Stokes solvers for modeling fluid dynamics offering advantages in computational efficiency, parallelization, and handling of complex boundaries. Despite these strengths, accurately reproducing compressible, shock-driven phenomena remains challenging. This study investigates the performance of LBM in simulating the Sod shock tube problem, a classical benchmark for compressible flow-using both single and double distribution function formulations across one- and two-dimensional lattice stencils. A MATLAB-based solver was developed to model the flow under isothermal conditions and compared to the analytical solution using the L2 norm error. The one-dimensional models achieved errors between 3.5% and 4.0%, while two-dimensional models produced slightly higher errors between 4.0 % and 4.5%, confirming that LBM can capture weakly compressible shock tube dynamics with strong qualitative agreement. However, achieving less than 1 % error and fully modeling compressible effects will require incorporating energy levels, energy transport, and an explicit treatment of the specific heat ratio (𝛾). This work provides a systematic assessment of LBM accuracy and stability, establishing a foundation for the future development of thermally coupled and fully compressible lattice Boltzmann solvers.

Recommended Citation

Schroeder, Timothy P. (2025) "Modeling of Supersonic Wave and Shock Propagation using the Lattice Boltzmann Method," Beyond: Undergraduate Research Journal: Vol. 9 , Article 10.
Available at: https://commons.erau.edu/beyond/vol9/iss1/10