Stable and accurate numerical modeling of seismic wave propagation in the vicinity of high-contrast interfaces is achieved with straightforward modifications to the conventional, rectangular-staggered-grid, finite-difference (FD) method. Improvements in material parameter averaging and spatial differencing of wavefield variables yield high-quality synthetic seismic data.
We present a mesh optimization algorithm for adaptively improving the finite element interpolation of a function of interest. The algorithm minimizes an objective function by swapping edges and moving nodes. Numerical experiments are performed on model problems. The results illustrate that the mesh optimization algorithm can reduce the W1,∞ semi-norm of the interpolation error. For these examples, the L2, L∞, and H1 norms decreased also.
This paper presents a new method for handling non-conforming hexahedralto- hexahedral interfaces. One or both of the adjacent hexahedralmeshes are locally modified to create a one-to-onemapping between between themesh nodes and quadrilaterals at the interface allowing a conforming mesh to be created. In the finite element method, non-conforming interfaces are currently handled using constraint conditions such as gapelements, tied contacts, or multi-point constraints. By creating a conforming mesh, the need for constraint conditions is eliminated resulting in a smoother, more precise numerical solution. The method presented in this paper uses hexahedral dual operations, including pillowing, sheet extraction, dicing and column collapse operations, to affect the local mesh modifications. In addition, an extension to pillowing, called sheet inflation, is introduced to handle the insertion of self-intersecting and self-touching sheets. The quality of the resultant conforming hexahedral mesh is high and the increase in number of elements is moderate.
A sub-scale experiment has been conducted to study the trailing vortex shed from a tapered fin installed on a wind tunnel wall to represent missile configurations. Stereoscopic particle image velocimetry measurements have been acquired in the near-field for several locations downstream of the fin tip and at different fin angles of attack. The vortex's tangential velocity is found to decay with downstream distance while its radius increases, but the vortex core circulation remains constant. Circulation and tangential velocity rise greatly for increased fin angle of attack, but the radius is approximately constant or slightly decreasing. The vortex axial velocity is always a deficit, whose magnitude diminishes with downstream distance and smaller angle of attack. No variation with Mach number can be discerned in the normalized velocity data. Vortex roll-up is observed to be largely complete by about four root chord lengths downstream of the fin trailing edge. Prior to this point, the vortex is asymmetric in the tangential velocity but the core radius stays nearly constant. Vortical rotation draws low-speed turbulent fluid from the wind tunnel wall boundary layer into the vortex core, which appears to hasten vortex decay and produce a larger axial velocity deficit than might be expected. Self-similarity of the vortex is established even while it is still rolling up. Attempts to normalize vortex properties by the fin's lift coefficient proved unsuccessful.
Error in Particle Image Velocimetry (PIV) interrogation due to velocity gradients in turbulent flows was studied for both classical and advanced algorithms. Classical algorithms are considered to be digital cross-correlation analysis including discrete window offsets and, for the present work, advanced algorithms are those using image deformation to compensate for velocity gradients. Synthetic PIV simulations revealed substantial negative biases in the turbulent stress for classical algorithms even for velocity gradients within recommended PIV design limits. This bias worsens if the distribution of velocity gradients has a nonzero mean, and error in the mean velocity may be introduced as well. Conversely, advanced algorithms do not exhibit this bias error if the velocity gradients are linear. Nonlinear velocity gradients increase the error in classical algorithms and a significant negative bias in the turbulent stress arises for the advanced algorithm as well. Two experimental data sets showed substantially lower turbulent stresses for the classical algorithm compared with the advanced algorithm, as predicted. No new experimental design rules for advanced algorithms are yet proposed, but any such recommendation would concern second-order velocity derivatives rather than first order.
We demonstrate the power of our technique for establishing and immobilizing well-defined polymer gradients in microchannels by fabricating two miniaturized analytical platforms: microscale immobilized pH gradients (μIPGs) for rapid and high resolution isoelectric focusing (IEF) applications, and polyacrylamide porosity gradients to achieve microscale pore limit electrophoresis (μPLE) in which species are separated based on molecular size by driving them toward the pore size at which migration ceases. Both separation techniques represent the first microscale implementation of their respective methodologies.