An implicit high-order radial basis function-based differential quadrature-finite volume method on unstructured grids to simulate incompressible flows with heat transfer

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

“…Owing to the high-order accuracy of the present TLBFS-FDQ method, the grid adopted here is significantly less than the ones reported in other works. 34,35,1 The normalised velocity and the temperature profiles for Pr = 0.71 and Ra = 100 with three different Re = (5, 20, 30) are plotted in Figure 10. Meanwhile, Figure 11 presents the normalised temperature profiles for Re = 10 and Ra = 100 with Pr = (0.2, 0.8, 1.5).…”

“…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.…”

Efficient resolution of incompressible Navier–Stokes equations using a robust high‐order pseudo‐spectral approach

“…Study for Reynolds number in the range $$$ \left[0,1000\right] $$$ of the Kovasznay flow is presented by using a Taylor meshless method and the ANM in Reference 33. Simulation of incompressible flows with heat transfer on unstructured mesh is made by a high‐order implicit radial basis function‐based differential quadrature‐finite volume (IRBFDQ‐FV) method in Reference 20. Radial basis function collocation method has been coupled with explicit time integration by Wang et al 21 to solve the incompressible (N‐S)‐equations under a weighted strong form.…”

“…The use of such a numerical approach could be limited or motivated by testing this factor. Among the best‐known meshless methods in the literature, we find Smooth Particle Hydrodynamics (SPH), 6‐8 Moving Least Squares (MLS) approximation, 2,9‐13 Reproducing Kernel Particle Method (RKPM), 14 Element‐Free Galerkin Methods (EFGM), 15 Taylor meshless method, 16 and Method of Fundamental Solutions (MFS), 17,18 Radial Basis Function 19‐21 …”

“…Among the best-known meshless methods in the literature, we find Smooth Particle Hydrodynamics (SPH), [6][7][8] Moving Least Squares (MLS) approximation, 2,[9][10][11][12][13] Reproducing Kernel Particle Method (RKPM), 14 Element-Free Galerkin Methods (EFGM), 15 Taylor meshless method, 16 and Method of Fundamental Solutions (MFS), 17,18 Radial Basis Function. [19][20][21] Regarding incompressible fluid flows, the need for careful software to treat the coupling between pressure and velocity fields in (N-S)-equations leads to develop mathematical models and numerical simulations as prediction means. These models differ from those that use the pressure-velocity formulation and those that eliminate pressure from the (N-S)-equations using several techniques 9,10,12,22 and other formulation which focus on the vorticity unknown.…”