individual
What campus are you from?
Daytona Beach
Authors' Class Standing
Timothy Schroeder, Senior
Lead Presenter's Name
Timothy Schroeder
Faculty Mentor Name
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 (š¯›¾). 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.
Did this research project receive funding support from the Office of Undergraduate Research.
No
Modeling of Supersonic Wave and Shock Propagation using the Lattice Boltzmann Method
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 (š¯›¾). 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.