A simulation of edge turbulence in the scrapeoff layer of tokamaks. The simulation represents the flow in the radial plasma density ρ, coupled to the vorticity and electrostatic potential run to 32,000 gyroperiods. The actual plot is a color map of the logdensity χ. This simulation was run to fourth order accuracy on 65536 finite elements using a discontinuous Galerkin formulation on 256 cores of TACCs stampede supercomputer. The ArcOn software was used to run this simlation.
Here we show a parametrization of the Brazos river estuary. On the left is the finite element mesh superimposed over a Googlemap. On the right is the corresponding bathymetry tracking the ocean topography. The problem studies the estuary eutrophication problem caused by fertilizer runoff in the Gulf of Mexico region.
This shows the penrichment of a solution meshed over the Brazos estuary of the gulf of Mexico. The solution retains the greatest resolution, using this particular penrichment scheme (which in this example is a fixed tolerance penrichment program), in areas of deep bathymetry, while near the river outlet, tidal inlets and coastline the p value is lowered. The chemistry of the solution tracks an esturay eutrophication study of a multicomponent flow following the phosphates (iota) present in fertilizer runoff upstream. See a movie of phosphate level tracking here (click).
On the left is a dioristic energy scheme for dynamic penrichment, based on a coupled global energy consistency. On the right is a similar dioristic energy scheme applied to element boundaries, where dynamic hadaptivity is achieved. These schemes are naturally coupled to provide dynamic hpadaptivity by way of dioristic energy.
Here we demonstrate the importance of setting proper boundary conditions in solutions to nonlinear systems of PDEs, showing the difference map in a solution of the quantum hydrodynamic (QHD) equations using a Dirichlet boundary condition set to the initial condition, versus a first order transmissive boundary condition. The difference between the two solutions quickly becomes much more pronounced given more realistic initialboundary data.
A graph of the evolution in time t of the concentrations of an n=5 fluid mixture of inert gases using a viscous compressile barotropic NavierStokes model comprised of: Ar, Kr, SO_{2}, O_{2} and H_{2}O at 293 Kelvin. Here we use periodic boundary conditions with a second order RungeKutta time integrator.
