High order approximations of the vortical flow field and resulting aerodynamic coefficients of complex supersonic vortical flows, are computed using the Implicit Parabolized Navier-Stokes solver (IMPNS). Third and fifth order Weighted Essentially Non-oscillating (WENO) schemes for evenly spaced and for stretched structured meshes are employed for the approximate Riemann solution of the inviscid cross flow fluxes. An approximate Riemann solution is obtained using the Osher and Solomon solver and the one-equation Spalart-Allmaras turbulence model is modified for an improved strain-vorticity approximation. Results indicate that even on much coarser meshes the 5$^\text{th}$ order PNS-WENO-Spalart-Allmaras approach may achieve results that are superior to previously published full Navier-Stokes solutions that employ a two-equation RANS model but the additional computational demand of schemes for non-uniform grids, may not be justifiable for smoothly varying meshes. The proposed PNS-WENO scheme combination provides a novel approach that is fast, accurate and robust, and that can substantially reduce numerical dissipation and improve the resolution of the vortical structures.

Microscopic level interaction between fusion-peptides and lipid bilayer membranes plays a crucial role in membrane fusion, a key step of viral infection. In this paper, we use coarse-grained molecular dynamics (CGMD) simulations to study the interaction between hemagglutinin fusion-peptides and phospholipid bilayer membranes. With CGMD, we are able to simulate the interaction of fusion peptides with a relatively large piece of membrane for a sufficiently long time period, which is necessary for a detailed understanding of the fusion process. A conformation of the peptide with a kink at the level of phosphate group is obtained, consistent with NMR and EPR studies. Our results show that the N-terminal segment of the peptide inserts more deeply into the membrane bilayer compared to the C-terminal segment, as observed in previous experiments. Our simulations also show that the presence of fusion peptides inside the membrane may cause bilayer thinning and lipid molecule disorder. Finally, our results reveal that peptides tend to aggregate, indicating cluster formation as seen in many experiments.

Large eddy simulation of the flow over a circular cylinder at Reynolds number Re_D=2580 has been studied with a high-order unstructured spectral difference method. Grid and polynomial refinement studies were carried out to assess numerical errors. The mean and fluctuating velocity fields in the wake of a circular cylinder were compared with PIV experimental measurements. The numerical results are in excellent agreement with the experimental data for both the mean velocity and Reynolds stresses using the high-order SD scheme. Other wake characteristics such as the recirculation bubble length, vortex formation length and maximum intensity of the velocity fluctuations have also been predicted accurately. The numerical simulations demonstrated the potential of the high-order SD method in accurate large eddy simulation of physically complex problems.

A lattice Boltzmann method is developed for modeling viscous elementary flows. An adjustable source term is added to the lattice Boltzmann equation, which can be tuned to model different elementary flow features like a doublet or a point source of any strength, including a negative source (sink). The added source term is dimensionally consistent with the lattice Boltzmann equation. The proposed model has many practical applications, as it can be used in the framework of the potential flow theory of viscous and viscoelastic fluids. The model can be easily extended to the three dimensional case. The model is verified by comparing its results with the analytical solution for some benchmark problems. The results are in good agreement with the analytical solution of the potential flow theory.

In this paper we compare different methods currently used in the stabilization of numerical simulations of time-dependent viscoelastic fluid flows described with the Oldroyd-B and related models. The methods under consideration, based on the separation of newtonian-like components from the stress tensor, are applied to a finite volume analysis of two simple benchmark problems (the plane Poiseuille startup and pulsated flows), for which analytical solutions are known. The relative performances of each method are evaluated regarding stability, accuracy and efficiency.

Direct numerical simulation (DNS) of incompressible flows in a zero-pressure gradient turbulent boundary layer (TBL) is conducted by a finite difference method in which a fourth order upwind scheme is applied to discretize the convective terms while a re-scaling approach is used to set inlet flow conditions. The Reynolds numbers based on free flow velocity and momentum thickness at the recycle section are respectively 687, 1074, and 1430. The DNS has obtained favorable results indicating that the turbulence statistics are quite satisfactory as compared with the existing numerical and experimental results. The three dimensional turbulent structures at the momentum thickness Reynolds number of 1430 in several different instants are illustrated by the iso-surface of swirl strength square (the square of imaginary part of the complex eigenvalue of velocity gradient tensor) together with velocity vectors in three different cross sections. It is found that there are three kinds of vortical structures: quasi-symmetrical and asymmetrical hairpin vortices, and worm-like vortices. The DNS based on the numerical method can certainly reveal the main characteristics of the TBL flows at the given Reynolds numbers.

Adaptive higher-order finite element methods ($hp$-FEM) are well known for their potential of exceptionally fast (exponential) convergence. However, most $hp$-FEM codes remain in an academic setting due to an extreme algorithmic complexity of $hp$-adaptivity algorithms. This paper aims at simplifying $hp$-adaptivity for $H$(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes. The technique is described and it is demonstrated numerically that it makes adaptive $hp$-FEM more efficient compared to $hp$-FEM on regular meshes and meshes with one-level hanging nodes.