The dependence of the computation of advective-diffusive transport phenomena on the orientation of the mesh with respect to the flow direction is analyzed. Poor performance of the classical Galerkin finite element method in the convectiondominated regime is alleviated by stabilization. We propose definitions of the stability parameter that rationally incorporate the flow direction. Numerical te...

The complex variable boundary-element method is routinely used to determine the complex potential, h 1⁄4 / þ iw, at any position, z 1⁄4 xþ iy, internal to the flow domain. We reverse this mapping by exactly determining the complex position for specified complex potentials––in effect solving for zðhÞ instead of hðzÞ. Direct calculation of the physical location, 1⁄2x; y , of potential, 1⁄2/;w , i...

We present hierarchical streamline bundles, a new approach to simplifying and visualizing 2D flow fields. Our method first densely seeds a flow field and produces a large number of streamlines that capture important flow features such as critical points. Then, we group spatially neighboring and geometrically similar streamlines to construct a hierarchy from which we extract streamline bundles a...

Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numerical tests are performed. The method is based on an unfitted discontinuous Galerkin approach where the surface is not explicitly tracked by the mesh which means the method is extremely flexible with respec...

Numerical solutions of convection–diffusion equations obtained using the Streamline–Upwind Petrov–Galerkin (SUPG) stabilisation typically possess spurious oscillations at layers. Spurious Oscillations at Layers Diminishing (SOLD) methods aim to suppress or at least diminish these oscillations without smearing the layers extensively. In the recent review by John and Knobloch (2007), numerical st...

A computational study is presented on cross-stream migration and focusing of deformable capsules in curved microchannels square rectangular sections under inertial non-inertial regimes. The numerical methodology based immersed boundary methods for fluid–structure coupling, a finite-volume-based flow solver finite-element method capsule deformation. Different behaviours the two regimes are predi...

Using a technique for constructing analytic expressions for discrete solutions to the convection-diffusion equation, we examine and characterize the effects of upwinding strategies on solution quality. In particular, for grid-aligned flow and discretization based on bilinear finite elements with streamline upwinding, we show precisely how the amount of upwinding included in the discrete operato...

The application of state-of-the-art history matching methods to large heterogeneous reservoirs is hampered by two main problems: (1) reservoir models should be constrained jointly to dynamic data and a large variety of geological continuity information, (2) CPU demand should not be prohibitive for large models. This paper proposes a method contributing to alleviating these two main concerns. By...