MRT lattice Boltzmann method for 2D flows in curvilinear coordinates

• The 2D flow equations are fully transformed into curvilinear coordinates.
• Obtained system of curvilinear flow equations is modeled using the MRT-LBM.
• The basic simple structure of the standard MRT-LBM method is maintained.
• The model is applied on physical and schematic domains of complex shape.
• Very good agreement between results and compared values is obtained.

Objective: The objective of the presented paper is establishing the multi-relaxation-time lattice Boltzmann method (MRT-LBM) for solving 2D flow equations transformed in a curvilinear coordinate system.Method: Using the complete transformation approach – which includes transformation of both dependent and independent variables between the physical and computational domain – corresponding forms of the equilibrium function and of the force term for the 2D Navier–Stokes equations and the shallow water equations have been derived. The physical flow domain of arbitrary geometry in the horizontal plane, is covered with adequate curvilinear mesh, while the calculation procedure is carried out in the D2Q9 square lattice, applying the basic form of the boundary condition method on water-solid and open boundaries as well.Test cases: The method is tested using four different examples: Couette flow in a straight inclined channel, Taylor–Couette flow between two cylinders, a non-prismatic channel in a 180° bend, and a segment of irrigation channel with a parabolic cross section in a 90° bend. In the cases of the bent channels, previously available velocity measurements have been used for validation of the model. In addition, the procedure employs a mathematical model based on traditional CFD procedures.Results: The remarkable agreement between the results obtained by the proposed model and the corresponding analytical values and measurements shows that the presented curvilinear form of the LBM is capable of solving very complex environmental problems, maintaining the order of accuracy, simplicity and efficiency of the basic LBM.