Based on our continuum hydrodynamic model for immiscible two-phase flows at solid surfaces, the stick-slip motion has been predicted for moving contact line at chemically patterned surfaces [Wang et al., J. Fluid Mech., 605 (2008), pp. 59-78]. In this paper we show that the continuum predictions can be quantitatively verified by molecular dynamics (MD) simulations. Our MD simulations are carried out for two immiscible Lennard-Jones fluids confined by two planar solid walls in Poiseuille flow geometry. In particular, one solid surface is chemically patterned with alternating stripes. For comparison, the continuum model is numerically solved using material parameters directly measured in MD simulations. From oscillatory fluid-fluid interface to intermittent stick-slip motion of moving contact line, we have quantitative agreement between the continuum and MD results. This agreement is attributed to the accurate description down to molecular scale by the generalized Navier boundary condition in our continuum model. Numerical results are also presented for the relaxational dynamics of fluid-fluid interface, in agreement with a theoretical analysis based on the Onsager principle of minimum energy dissipation.

Over the last decade the Lattice Boltzmann Method (LBM) has gained significant interest as a numerical solver for multiphase flows. However most of the LB variants proposed to date are still faced with discreteness artifacts in the form of spurious currents around fluid-fluid interfaces. In the recent past, Lee et al. have proposed a new LB scheme, based on a higher order differencing of the non-ideal forces, which appears to virtually free of spurious currents for a number of representative situations. In this paper, we analyze the Lee method and show that, although strictly speaking, it lacks exact mass conservation, in actual simulations, the mass-breaking terms exhibit a self-stabilizing dynamics which leads to their disappearance in the long-term evolution. This property is specifically demonstrated for the case of a moving droplet at low-Weber number, and contrasted with the behaviour of the Shan-Chen model. Furthermore, the Lee scheme is for the first time applied to the problem of gravity-driven Rayleigh-Taylor instability. Direct comparison with literature data for different values of the Reynolds number, shows again satisfactory agreement. A grid-sensitivity study shows that, while large grids are required to converge the fine-scale details, the large-scale features of the flow settle-down at relatively low resolution. We conclude that the Lee method provides a viable technique for the simulation of Rayleigh-Taylor instabilities on a significant parameter range of Reynolds and Weber numbers.

We are interested in the modeling of wave propagation in an infinite bilayered acoustic/poroelastic media. We consider the biphasic Biot's model in the poroelastic layer. The first part was devoted to the calculation of analytical solution in two dimensions, thanks to Cagniard de Hoop method. In the first part (Diaz and Ezziani, Commun. Comput. Phys., Vol. 7, pp. 171-194) solution to the two-dimensional problem is considered. In this second part we consider the 3D case.

We present a model for simulating wave propagation in stratified magneto-atmospheres. The model is based on equations of ideal MHD together with gravitational source terms. In addition, we present suitable boundary data and steady states to model wave propagation. A finite volume framework is developed to simulate the waves. The framework is based on HLL and Roe type approximate Riemann solvers for numerical fluxes, a positivity preserving fractional steps method for discretizing the source and modified characteristic and Neumann type numerical boundary conditions. Second-order spatial and temporal accuracy is obtained by using an ENO piecewise linear reconstruction and a stability preserving Runge-Kutta method respectively. The boundary closures are suitably modified to ensure mass balance. The numerical framework is tested on a variety of test problems both for hydrodynamic as well as magnetohydrodynamic configurations. It is observed that only suitable choices of HLL solvers for the numerical fluxes and balanced Neumann type boundary closures yield stable results for numerical wave propagation in the presence of complex magnetic fields.

An efficient implicit procedure for the Discontinuous Galerkin (DG) method is developed utilizing a pointwise relaxation algorithm. In the pointwise relaxation, those contributions from the degrees of freedom in own computational cell are accounted for in the implicit matrix inversion. The resulting scheme is shown to be stable with very large CFL numbers for both the Euler and the Navier-Stokes equations for typical test problems. In order to achieve a faster convergence, efforts are also made to reduce computing time of the present method by utilizing a p-multigrid scheme and also by solving a simplified matrix instead of a fully loaded dense matrix in the implicit matrix inversion. A superior performance of the present implicit DG method on the parallel computer using up to 128 PEs is shown in terms of readily achievable scalability and high parallel efficiency. The RANS simulation of turbulent flowfield over AGARD-B model is carried out to show the convergence property and numerical stability of the present implicit DG method for engineering applications.

In this paper, we investigate by numerical simulations the Bak-Sneppen model (BSM) for biological evolution on scale-free networks (SFNs) with various degree exponents γ. We find that the punctuated equilibrium is rather robust with respect to the network topology. Furthermore, we analyze the evolution of the critical average fitness <f>_∗ and the exponent τ of <f>₀ avalanche as a function of α (i.e., the degree exponent γ). Our observations indicate the dependence of evolutionary dynamics of BSM on the complex biosystem topology.

In this paper, we propose a lattice Boltzmann (LB) method coupled with a direct-forcing fictitious domain (DF/FD) method for the simulation of particle suspensions. This method combines the good features of the LB and the DF/FD methods by using two unrelated meshes, namely, an Eulerian mesh for the flow domain and a Lagrangian mesh for the solid domain, which avoids the re-meshing procedure and does not need to calculate the hydrodynamic forces at each time step. The non-slip boundary condition is enforced by introducing a forcing term into the lattice Boltzmann equation, which preserves all remarkable advantages of the LBM in simulating fluid flows. The present LB-DF/FD method has been validated by comparing its results with analytical results and previous numerical results for a single circular particle and two circular particles settling under gravity. The interaction between particle and wall, the process of drafting-kissing-tumbling (DKT) of two settling particles will be demonstrated. As a manifestation of the efficiency of the present method, the settling of a large number (128) of circular particles is simulated in an enclosure.

The guided and leaky modes of a planar dielectric waveguide are eigensolutions of a singular Sturm-Liouville problem. The modes are the roots of a characteristic function which can be found with several methods that have been introduced in the past. However, the evaluation of the characteristic function suffers from numerical instabilities, and hence it is often difficult to find all modes in a given range. Here a new variational formulation is introduced, which, after discretization, leads either to a quadratic or a quartic eigenvalue problem. The modes can be computed with standard software for polynomial eigenproblems. Numerical examples show that the method is numerically stable and guarantees a complete set of solutions.

We numerically simulate a photonics phenomenon of what we call intensity inversion between red and green fluorescence in oxyfluoride nanophase vitroceramics Er(1%)Yb(8%): FOV through the integration of whole fluorescence's theories. We found that it is essential to introduce a coefficient presenting the difference between the Stokes energy transfer and anti-Stokes energy transfer processes in nano-material when calculating the energy transfer rate. Under this consideration, and with the total crystallized volume ratio set to be 17.6%, the simulation results of the population probabilities values of all energy levels of Er³⁺ ion are coincident with the experimental result perfectly.

We consider the multi-scale modeling of the isothermal chemical vapor infiltration (CVI) process for the fabrication of C/SiC composites. We first present a microscopic model in which the preform is regarded as a two-phase porous media described by a dynamic pore-scale node-bond network during the fabrication process. We then develop a macroscopic model by a upscaling procedure based on the homogenization theory.

The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplectic Fourier spectral (MSFS) methods will be employed to solve the fourth-order Schrödinger equations with trapped term. Using the idea of split-step numerical method and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventional multi-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.

The goal of efficient and robust error control, through local mesh adaptation in the computational solution of partial differential equations, is predicated on the ability to identify in an a posteriori way those localized regions whose refinement will lead to the most significant reductions in the error. The development of a posteriori error estimation schemes and of a refinement infrastructure both facilitate this goal, however they are incomplete in the sense that they do not provide an answer as to where the maximal impact of refinement may be gained or what type of refinement — elemental partitioning (h-refinement) or polynomial enrichment (p-refinement) — will best lead to that gain. In essence, one also requires knowledge of the sensitivity of the error to both the location and the type of refinement. In this communication we propose the use of adjoint-based sensitivity analysis to discriminate both where and how to refine. We present both an adjoint-based and an algebraic perspective on defining and using sensitivities, and then demonstrate through several one-dimensional model problem experiments the feasibility and benefits of our approach.