A two‐step Taylor‐characteristic‐based Galerkin method for incompressible flows and its application to flow over triangular cylinder with different incidence angles

Abstract

SUMMARYAn alternative characteristic-based scheme, the two-step Taylor-characteristic-based Galerkin method is developed based on the introduction of multi-step temporal Taylor series expansion up to second order along the characteristic of the momentum equation. Contrary to the classical characteristic-based split (CBS) method, the current characteristic-based method does not require splitting the momentum equation, and segregate the calculation of the pressure from that of the velocity by using the momentum-pressure Poisson equation method. Some benchmark problems are used to examine the effectiveness of the proposed algorithm and to compare with the original CBS method, and the results show that the proposed method has preferable accuracy with less numerical dissipation.We further applied the method to the numerical simulation of flow around equilateral triangular cylinder with different incidence angles in free stream. In this numerical investigation, the flow simulations are carried out in the low Reynolds number range. Instantaneous streamlines around the cylinder are used as a means to visualize the wake region behind, and they clearly show the flow pattern around the cylinder in time. The influence of incidence angle on flow characteristic parameters such as Strouhal number, Drag and Lift coefficients are discussed quantitatively.

Laminar Flow Patterns Around Three Side-By-Side Arranged Circular Cylinders Using Semi-Implicit Three-Step Taylor-Characteristic-Based-Split (3-TCBS) Algorithm

“…The one-dimensional form of the developed threestep Taylor-characteristic-based-split scheme (3-TCBS) scheme starts from equation (4). It is well known that any function f n+θ belonging to the θ-families and defined as f n+θ = (1-θ) f n + θf n+1 can become the Crank-Nicolson form with a better accuracy in time with the parameter θ=1/2.…”

Flow characteristics of two in-phase oscillating cylinders in side-by-side arrangement

“…The original fractional step method is known to be of the first-order time accurate in pressure solution due to the splitting error introduced if the pressure term is completely removed from the momentum equation at the splitting stage [47][48][49]. Recently, the issue on elimination of the first-order time error in pressure has attracted wider attention and some improved schemes with second-order time-accurate in pressure have been developed [27,50,51]. In this paper, a second-order characteristic-based-split finite element method [27] with MINI triangular element discretization (CBS/MINI) is extended to the Arbitrary Lagrangian-Eulerian (ALE) formulation [28] to account for bodymotion in the flow field.…”

A Galerkin finite element algorithm based on third‐order Runge‐Kutta temporal discretization along the uniform streamline for unsteady incompressible flows

“…However, for unsteady flow, the stability condition of the dual‐time stepping procedure and the choice of the AC parameter can become too restrictive, even leading to slow convergence rates. Based on the midpoint method, Bao and Zhou and Enjilela and Arefmanesh further proposed the two‐step method, hybrid MINI element, and pressure projection method in order to improve the accuracy of the CBS method and stable the pressure field, but the two‐step method needs to update total element matrix twice in each time step, which reduce calculation efficiency. In order to further improve calculation accuracy, Drikakis et al used the classic Runge‐Kutta method for temporal discretization, but spacial discretization is based on the upwind difference scheme to stabilize the pressure field.…”

“…In order to further improve calculation accuracy, Drikakis et al used the classic Runge‐Kutta method for temporal discretization, but spacial discretization is based on the upwind difference scheme to stabilize the pressure field. Based on the Runge‐Kutta temporal discretization along the streamline, Zhang et al proposed a characteristic‐based Galerkin FEM, but its calculation efficiency is equivalent to the two‐step method and needs to be further improved.…”