High-order flux reconstruction thermal lattice Boltzmann flux solver for simulation of incompressible thermal flows

Development of a Fourier‐expansion based differential quadrature method with lattice Boltzmann flux solvers: Application to incompressible isothermal and thermal flows

“…It is noted that at larger Ks, the errors are bounded by certain limits, which is due to the intrinsic compressibility error for LBM and LBM-based methods. 26,27,14 On the other hand, the present LBFS-FDQ results converge to grid independent solution much faster. Namely, for reaching same level of accuracy, the present LBFS-FDQ method requires fewer grid points.…”

“…It is also worth mentioning that the CPU time for simulating the double shear flows as listed in Table 4 is considerably lower than that reported by others. 29,31,14 Although a more rigorous efficiency comparison should also take other factors such as differences in hardware, programming language, code implementation and optimisation into consideration, the reduction of CPU time from hours (as reported in References 29,31,14) to minutes and seconds (for the present work) while maintaining good accuracy is still remarkable for the present LBFS-FDQ method.…”

“…In other words, by linearly adding more grid points in the FDQ discretization, the numerical solution approximates the analytical solution much better and the exponential convergence rate can be achieved. It is noted that at larger $$$ K $$$s, the errors are bounded by certain limits, which is due to the intrinsic compressibility error for LBM and LBM‐based methods 26,27,14 . On the other hand, the present LBFS‐FDQ results converge to grid independent solution much faster.…”

“…Two Reynolds numbers, that is, Re = 10 3 and 10 4 , are simulated in the present work to test the accuracy and stability of the LBFS-FDQ method. To compare the present results with reference data in the literature, the Re = 10 3 case are tested with w = 80, 𝛿 = 0.05 and b = 0.25, 26,29,30,14 whereas w = 30, 𝛿 = 0.05 and b = 0 are used for the Re = 10 4 simulations. [31][32][33] The flow at Re = 10 3 is computed with the grid sizes of 31 × 31 and 51 × 51.…”

“…Endeavours have been made to improve the accuracy order of LBFS. Specifically, LBFS is combined with the HO least-square-based finite-difference-FV (LSFD-FV), [8][9][10][11] radial basis function-based differential quadrature-FV (RBFDQ-FV) 1,12 and flux reconstruction 13,14 methods. The present authors recently propose a high-order generalised differential quadrature method with LBFS (LBFS-GDQ) 15 for incompressible isothermal flows, which adopts the HO polynomial-based generalised differential quadrature (GDQ) discretization to solve the governing equations recovered by LBFS.…”