Semi-Lagrangian lattice Boltzmann method for compressible flows
Dominik Wilde1,2, Andreas Krämer3, Dirk Reith2,4
1Department of Mechanical Engineering, University of Siegen, Paul-Bonatz-Straße 9-11, D-57076 Siegen-Weidenau, Germany.
Physical Review. E
|June 25, 2020
Summary
A new semi-Lagrangian lattice Boltzmann (SLLBM) solver accurately simulates compressible flows, including supersonic speeds. This method uses cell-based interpolation for high-order spatial accuracy and minimal mass loss, proving effective in complex flow simulations.
Area of Science:
- Computational fluid dynamics
- Numerical methods for fluid flow
- High-performance computing
Background:
- Traditional lattice Boltzmann methods (LBM) face challenges in accurately simulating compressible flows.
- Existing LBM solvers for compressible flows often require complex grid structures or exhibit limited Galilean invariance.
- The need for robust and accurate numerical methods for supersonic and transonic flow regimes is critical in various engineering applications.
Purpose of the Study:
- To develop and validate a novel semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows.
- To enhance spatial accuracy and minimize mass loss in LBM simulations through advanced interpolation techniques.
- To demonstrate the solver's capability in handling supersonic flows and its Galilean invariance.
Main Methods:
- Implementation of a cell-based interpolation scheme using polynomials up to fourth order.
- Utilizing Gauss-Lobatto-Chebyshev support points for distribution function values.
- Employing integration along characteristics for independent time step size selection.
- Testing with diverse flow scenarios including Taylor-Green vortex, Sod shock tube, Riemann problem, and shock-vortex interaction.
Main Results:
- The SLLBM solver successfully simulates compressible flows, including supersonic regimes.
- High-order spatial accuracy and significantly reduced mass loss were achieved due to cell-based interpolation.
- The method exhibits a high degree of Galilean invariance, operating in a static reference frame.
- Demonstrated applicability to nonuniform grids through transformed grids in shock-vortex interaction simulations.
Conclusions:
- The developed SLLBM solver offers a robust and accurate approach for compressible flow simulations.
- Cell-based interpolation and specific support points are key to achieving high-order accuracy and minimizing numerical artifacts.
- The solver's capabilities extend to complex phenomena like shock-vortex interactions and can be applied to non-uniform grids.
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