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Summary
The paper proposes a new lattice Boltzmann scheme with a projection step, extending the multiresolution relaxation times (MRT) lattice Boltzmann scheme. The new scheme is analyzed and compared to the classic MRT scheme, showing improved stability and accuracy.
Highlights
- The new scheme is based on a projection operator that decomposes the moments into conserved and non-conserved components.
- The projection step does not change the asymptotic partial differential equations at second order.
- The new scheme is more stable than the classic MRT scheme, allowing for a wider range of relaxation parameters.
- The scheme is tested on several numerical examples, including the Minion-Brown test case and the lid-driven cavity.
- The results show improved accuracy and stability compared to the classic MRT scheme.
- The new scheme can be used to simulate fluid flows with high Reynolds numbers.
- The paper provides a theoretical analysis of the new scheme, including a proof of the proposition.
Key Insights
- The introduction of the projection step in the lattice Boltzmann scheme improves the stability and accuracy of the method, allowing for a wider range of relaxation parameters.
- The new scheme is able to capture the correct physics of fluid flows, including the behavior of the viscous stress tensor and the energy transfer moments.
- The use of the projection operator simplifies the relaxation process and reduces the number of parameters needed to be tuned.
- The new scheme can be used to simulate complex fluid flows, including those with high Reynolds numbers and non-linear dynamics.
- The theoretical analysis of the new scheme provides a deeper understanding of the underlying physics and the behavior of the method.
- The results of the numerical examples demonstrate the improved accuracy and stability of the new scheme compared to the classic MRT scheme.
- The new scheme has the potential to be used in a wide range of applications, including engineering and scientific simulations.
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Citation
Dubois, F., & Philippi, P. C. (2024). Multiresolution relaxation times lattice Boltzmann schemes with projection (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.17426