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We present a hybrid spectral element-Fourier spectral method for solving the coupled system of Navier-Stokes and Cahn-Hilliard equations to simulate wall-bounded two-phase flows in a three-dimensional domain which is homogeneous in at least one direction. Fourier spectral expansions are employed along the homogeneous direction and $C^0$ high-order spectral element expansions are employed in the other directions. A critical component of the method is a strategy we developed in a previous work for dealing with the variable density/viscosity of the two-phase mixture, which makes the efficient use of Fourier expansions in the current work possible for two-phase flows with different densities and viscosities for the two fluids. The attractive feature of the presented method lies in that the two-phase computations in the three-dimensional space are transformed into a set of de-coupled two-dimensional computations in the planes of the non-homogeneous directions. The overall scheme consists of solving a set of de-coupled two-dimensional equations for the flow and phase-field variables in these planes. The linear algebraic systems for these two-dimensional equations have constant coefficient matrices that need to be computed only once and can be pre-computed. We present ample numerical simulations for different cases to demonstrate the accuracy and capability of the presented method in simulating the class of two-phase problems involving solid walls and moving contact lines.
We explore the role of gravitational settling on inertial particle concentrations in a wall-bounded turbulent flow. While it may be thought that settling can be ignored when the settling parameter $Svequiv v_s/u_tau$ is small ($v_s$ - Stokes settling
We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex, heterogeneous, and no
Emerging commercial and academic tools are regularly being applied to the design of road and race cars, but there currently are no well-established benchmark cases to study the aerodynamics of race car wings in ground effect. In this paper we propose
A new scaling is derived that yields a Reynolds number independent profile for all components of the Reynolds stress in the near-wall region of wall bounded flows, including channel, pipe and boundary layer flows. The scaling demonstrates the importa
On its way to turbulence, plane Couette flow - the flow between counter-translating parallel plates - displays a puzzling steady oblique laminar-turbulent pattern. We approach this problem via Galerkin modelling of the Navier-Stokes equations. The wa