High-order simulation scheme for active particles driven by stress boundary conditions.

We study the dynamics and interactions of elliptic active particles in a two dimensional solvent. The particles are self-propelled through prescribing a fluid stress at one half of the fluid-particle boundary. The fluid is treated explicitly solving the Stokes equation through a discontinuous Galerkin scheme, which allows to simulate strictly incompressible fluids. We present numerical results for a single particle and give an outlook on how to treat suspensions of interacting active particles.

Long wavelength approximation to peristaltic motion of an Oldroyd 4-constant fluid in a planar channel.

An analysis is carried out to study the peristaltic motion of an incompressible Oldroyd 4-constant fluid in a planar channel. The flow modeling is first developed in dimensionless form and the governing problem is then simplified by adopting a long wavelength assumption. It is found that unlike Oldroyd 3-constant fluid, the governing problem of an Oldroyd 4-constant fluid under a long wavelength approximation contains the rheological parameters. The resulting non-linear problem has been solved numerically using a combination of the finite difference scheme and the iterative method. In addition, an analytical solution is presented for the domain near the channel center. The effect of material parameters on the pumping and trapping is discussed. A comparison with the corresponding results for a viscous Newtonian fluid is also made.

Direct numerical simulation of stochastically forced laminar plane couette flow: peculiarities of hydrodynamic fluctuations.

The background of three-dimensional hydrodynamic (vortical) fluctuations in a stochastically forced, laminar, incompressible, plane Couette flow is simulated numerically. The fluctuating field is anisotropic and has well pronounced peculiarities: (i) the hydrodynamic fluctuations exhibit nonexponential, transient growth; (ii) fluctuations with the streamwise characteristic length scale about 2 times larger than the channel width are predominant in the fluctuating spectrum instead of streamwise constant ones; (iii) nonzero cross correlations of velocity (even streamwise-spanwise) components appear; (iv) stochastic forcing destroys the spanwise reflection symmetry (inherent to the linear and full Navier-Stokes equations in a case of the Couette flow) and causes an asymmetry of the dynamical processes.

Solution of functional equations and reduction of dimension in the local energy transfer theory of incompressible, three-dimensional turbulence.

It is shown that the set of integrodifferential and algebraic functional equations of the local energy transfer theory may be considerably reduced in dimension for the case of isotropic turbulence. This is achieved without restricting the solution space. The basis for this is a complete analytical solution to the functional equations Q(k;t,t('))=H(k;t,t('))Q(k;t('),t(')) and H(k;t,s)H(k;s,t('))=H(k;t,t(')). The solution is proved to depend only on a single function straight phi(k;t) solely determining Q and H. Hence the dimension of both the dependent and the independent variables is reduced by one. From the latter, the corresponding two integrodifferential equations are lowered to a single integrodifferential equation for straight phi(k;t), extended by an integral side condition on the k dependence of straight phi(k;t). In the limit nu-->0, a partial solution to the reduced set of equations is presented in the Appendix.