A cell‐based smoothed finite element method with semi‐implicit CBS procedures for incompressible laminar viscous flows

Abstract

SummaryIn this paper, the cell-based smoothed finite element method (CS-FEM) with the semi-implicit characteristic-based split (CBS) scheme (CBS/CS-FEM) is proposed for computational fluid dynamics. The 3-node triangular (T3) element and 4-node quadrilateral (Q4) element are used for present CBS/CS-FEM for two-dimensional flows. The 8-node hexahedral element (H8) is used for three-dimensional flows.Two types of CS-FEM are implemented in this paper. One is standard CS-FEM with quadrilateral gradient smoothing cells for Q4 element and hexahedron cells for H8 element. Another is called as n-sided CS-FEM (nCS-FEM) whose gradient smoothing cells are triangles for Q4 element and pyramids for H8 element. To verify the proposed methods, benchmarking problems are tested for two-dimensional and three-dimensional flows. The benchmarks show that CBS/CS-FEM and CBS/nCS-FEM are capable to solve incompressible laminar flow and can produce reliable results for both steady and unsteady flows. The proposed CBS/CS-FEM method has merits on better robustness against distorted mesh with only slight more computation time and without losing accuracy, which is important for problems with heavy mesh distortion. The blood flow in carotid bifurcation is also simulated to show capabilities of proposed methods for realistic and complicated flow problems.

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

“…The circle cylinder is of unit diameter and is placed in the region Ω, where we choose three region sizes to validate and discuss, as shown in Table 4. The cylinder center lies at the origin of Cartesian system, the boundary conditions of flow past a circle cylinder are shown in Figure 10A 20,20] is divided into 21 104 linear structured elements with 4 nodes. The mesh is refined close to the cylinder surface, the nodal point number on the cylinder is 176, and the minimum element size is 0.015, which is in the radial direction of the elements adjacent to the cylinder, as shown in Figure 10B…”

“…Considering that the traditional CBS method is a single‐step method and has only first‐order accuracy, many researchers make the effort to develop it further . Nithiarasu et al developed a fully explicit and semiimplicit CBS method to different applications as a unified approach to fluid dynamics problems, known as the CBS‐AC (artificial compressibility) scheme, which takes advantage of both standard AC and velocity correction approaches.…”

“…[16][17][18] Considering that the traditional CBS method is a single-step method and has only first-order accuracy, many researchers make the effort to develop it further. [19][20][21] Nithiarasu et al 22-24 developed a fully explicit and semiimplicit CBS method to different applications as a unified approach to fluid dynamics problems, known as the CBS-AC (artificial compressibility) scheme, which takes advantage of both standard AC and velocity correction approaches. Based on the CBS-AC scheme, Konozsy and Dimitris 25 developed a unified fractional-step and pressure-projection method, He et al 26 further obtained the AC-CBS-based partitioned semiimplicit coupling algorithm through using stabilized second-order pressure scheme.…”

A smoothed finite element approach for computational fluid dynamics: applications to incompressible flows and fluid–structure interaction

“…3, the contribution of four SCs and GPs per Q4 element successfully circulates within one recurrence. Compared to [38], we organize the smoothed element integral into a more comprehensible pattern.…”

“…For this reason, the underlying investments may be discouraged from CFD. Most recently, we have witnessed a joyful breakthrough that makes the cell-based smoothed FEM (CS-FEM) accessible to incompressible NS equations in terms of three schemes to interpolate nodal quantities involving the mixed product [38].…”