In this article a finite volume method is proposed to solve viscous incompressible Navier-Stokes equations in two-dimensional regions with corners and curved boundaries. A hybrid collocated-grid variable arrangement is adopted, in which the velocity and pressure are stored at the centroid and the circumcenters of the triangular control cell, respectively. The cell flux is defined at the mid-point of the cell face. Second-order implicit time integration schemes are used for convection and diffusion terms. The second-order upwind scheme is used for convection fluxes. The present method is validated by results of several viscous flows.
This paper deals with the effects of traffc bottlenecks using an extended Lighthill-Whitham-Richards (LWR) model. The solution structure is analytically indicated by the study of the Riemann problem characterized by a discontinuous flux. This leads to a typical solution describing a queue upstream of the bottleneck and its width and height, and informs the design of a δ-mapping algorithm. More significantly, it is found that the kinetic model is able to reproduce stop-and-go waves for a triangular fundamental diagram. Some simulation examples, which are in agreement with the analytical solutions, are given to support these conclusions.
In the paper, a numerical study on symmetrical and asymmetrical laminar jet-forced flows is carried out by using a lattice Boltzmann method (LBM) with a special boundary treatment. The simulation results are in very good agreement with the available numerical prediction. It is shown that the LBM is a competitive method for the laminar jet-forced flow in terms of computational effciency and stability.
This paper presents a hybrid finite volume/finiteelement method for the incompressible generalized Newtonianfluid flow (Power-Law model). The collocated (i.e.non-staggered) arrangement of variables is used on theunstructured triangular grids, and a fractional step projectionmethod is applied for the velocity-pressure coupling.The cell-centered finite volume method is employed to dis-cretizethe momentum equation and the vertex-based finiteelement for the pressure Poisson equation. The momentuminterpolation method is used to suppress unphysical pressurewiggles. Numerical experiments demonstrate that the currenthybrid scheme has second order accuracy in both space andtime. Results on flows in the lid-driven cavity and betweenparallel walls for Newtonian and Power-Law models are alsoin good agreement with the published solutions.
This article presents a numerical investigation on a steady non-Newtonian flow through a two-dimensional channel with double constrictions. The power-law mode is employed in describing the non-Newtonian behavior of the flow. An unstructured finite volume method combined with a fractional-step projection method is developed for the discretization of incompressible equations governing the non-Newtonian flows. The important flow dynamics related with the arterial diseases, such as the wall shear stress and vortex generation, are also numerically studied in detail. Numerical results reveal that there are marked differences between Newtonian and non-Newtonian models.
We propose a new characteristic-based finite volume scheme combined with the method of Central Weighted Essentially Non-Oscillatory(CWENO) reconstruction and characteristics,to solve shallow water equations.We apply the scheme to simulate dam-break problems.A number of challenging test cases are considered,such as large depth differences even wet/dry bed.The numerical solutions well agree with the analytical solutions.The results demonstrate the desired accuracy,high-resolution and robustness of the presented scheme.
In this paper,a high-order finite-volume scheme is presented for the one-dimensional scalar and inviscid Euler conservation laws.The Simpson’s quadrature rule is used to achieve high-order accuracy in time.To get the point value of the Simpson’s quadrature,the characteristic theory is used to obtain the positions of the grid points at each sub-time stage along the characteristic curves,and the third-order and fifth-order central weighted essentially non-oscillatory(CWENO) reconstruction is adopted to estimate the cell point values.Several standard one-dimensional examples are used to verify the high-order accuracy,convergence and capability of capturing shock.
