We discuss a numerical 3D radiation-MHD simulation of penumbral fine structure in a small sunspot. This simulation shows the development of short filamentary structures with horizontal flows, similar to observed Evershed flows, and an inward propagation of these structures at a speed compatible with observations. Although the lengths of these filaments are much shorter than observed, we conject...

Motivated by studies of the cylinder wake, in which the vortex-shedding frequency can be obtained from the mean flow, we study thermosolutal convection driven by opposing thermal and solutal gradients. In the archetypal two-dimensional geometry with horizontally periodic and vertical no-slip boundary conditions, branches of traveling waves and standing waves are created simultaneously by a Hopf...

In this paper we apply the finite difference method on adaptive sparse grids [9] to the simulation of turbulent flows. This method combines the flexibility and efficiency of finite difference schemes with the advantages of an adaptive approximation by tensor product multiscale bases. We shortly discuss the method. Then, we present numerical results for a simple linear convection problem for a v...

The Boussinesq equations for Rayleigh–Bénard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to timedependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25000, the axisymmetric flow becomes unstable to standing or travelling azimu...

An analysis is performed to study the heat transfer characteristics of steady mixed convection flow over a permeable vertical flat plate embedded in an anisotropic fluid-saturated porous medium. The effects of uniform suction and injection on the flow field and heat transfer characteristics are numerically studied by employing an implicit finite difference Keller-box method. It is found that du...

An algebraic approach to the design of multidimensional high-resolution schemes is introduced and elucidated in the finite element context. A centered space discretization of unstable convective terms is rendered local extremum diminishing by a conservative elimination of negative off-diagonal coefficients from the discrete transport operator. This modification leads to an upwind-biased low-ord...

Helioseismic observations have detected small temporal variations of the rotation rate below the solar surface that correspond to the so-called "torsional oscillations" known from Doppler measurements of the surface. These appear as bands of slower- and faster-than-average rotation moving equatorward. Here we establish, using complementary helioseismic observations over 4 yr from the GONG netwo...

We present high-resolution numerical simulations of convection in multiphase flows (boiling) using a novel algorithm based on a lattice Boltzmann method. We first study the thermodynamical and kinematic properties of the algorithm. Then, we perform a series of 3D numerical simulations changing the mean properties in the phase diagram and compare convection with and without phase coexistence at ...

In this paper we consider various blends of implicit and explicit time integration schemes based on the well-known BDF2 method, applied to convection-diffusion problems with dominating convection. A fully implicit treatment of convection terms is often not very efficient. We shall deal with schemes that are implicit in the convection terms only locally in space, without introducing the internal...

Free convection flow in an enclosure filled with a congealing melt leads to the product with a nonuniform structure involving large grains. The convective flows are decreased by applying an appropriate magnetic field, obtaining uniform and small grain structures. In this work, using the finite volume method, we investigated the application of a magnetic field to the convective heat transfer and...