Abstract
In this paper, we develop a new computational framework to investigate the sloshing free surface flow of Newtonian and non-Newtonian fluids in the rectangular tanks. We simulate the flow via a two-phase model and employ the fixed unstructured mesh in the computation to avoid the mesh distortion and reconstruction. As for the solution of Navier–Stokes equation, we utilize the SUPG finite element method based on the splitting scheme. The same order interpolation functions are then used for velocity and pressure. Moreover, the moving interface is captured via the concise level set method. We take advantage of the implicit discontinuous Galerkin method to handle the solution of level set and its reinitialization equations. A mass correction technique is also added to ensure the mass conservation property. The dam break-free surface flow is simulated firstly to demonstrate the validity of our mathematical model. In addition, the sloshing Newtonian fluid in the tank with flat and rough bottoms is considered to illustrate the feasibility and robustness of our computational scheme. Finally, the development of free surface for non-Newtonian fluid is also studied in the two tanks, and the influence of power-law index on the sloshing fluid flow is analyzed.
Highlights
Simulation. ey considered dummy particles and a new way to handle the moving boundary
The elliptic subequations are solved via standard FEM for the high efficiency. e streamline upwind/Petrov–Galerkin (SUPG) method [14, 15] is utilized to solve the hyperbolic subequation for the stability. e same order interpolation functions are used for the velocity and pressure
The water is sustained in the region of (0,1) × (0,1) and a 1 m. e nonslip boundary conditions are used for the velocity on the solid walls
Summary
Simulation. ey considered dummy particles and a new way to handle the moving boundary. It is difficult to handle the boundary condition and the irregular computational domain for the mesh-free method. In the past several decades, the standard particle finite element method (PFEM) [9,10,11] is proposed and has been used for the simulation of free surface fluid flow. Mathematical Problems in Engineering et al [12] developed a Lagrangian elemental FEM to study the free surface flow. In 2020, Franci et al [13] have proposed another Lagrangian nodal integration method to simulate the free surface flow. We compare the development of free surface for different cases and analyze the influence of power-law index on it; in Section 5, we give the summary of the concluding remarks
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