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Titlebook: Computational Fluid Dynamics; Finite Difference Me Guoxiang Hou,Caikan Chen,Kai Wang Book 2024 The Editor(s) (if applicable) and The Author

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A Simplified Lattice Boltzmann Flux Solver of Multiphase Flowsg the numerical accuracy and stability of the original MLBFS. We test the simplified MLBFS on the Laplace law and the Rayleigh–Taylor instability problems and show that it can reduce the computation time by up to 18.32% compared to the original method.
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The Compatibility, Convergence, and Stability of Difference Schemesete perturbation method, energy method, and Hirt heuristic method, to analyse the numerical stability. Besides, a simple method using difference operator transform to calculate the transition factor is proposed, and an adequate discussion about various forms of stability conditions and the Lax equivalence theorem is given.
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Variable Coefficients and Nonlinear Problems. For the nonlinear partial differential equations, stability analysis and error estimation for nonlinear problems are more complex than linear problems. At the end of this chapter, the conservative difference scheme is discussed and analyzed using the controlling volume method based on the physical conservation law.
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Coupled Simplified Lattice Boltzmann Method Study on Thermal Flowsts. Four representative dimensionless heated lengths between 0 and 1, and typical temperature gradient orientations, namely vertical upward are selected to investigate the joint effects of the Richardson number, temperature gradient orientation, and length of the heat source on heat transfer.
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