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A phase-field model for the Hele-Shaw flow of non-Newtonian fluids is developed. It extends a previous model for Newtonian fluids to a wide range of shear-dependent fluids. The model is applied to perform simulations of viscous fingering in…
We analyze particle velocity fluctuations in a simulated granular system subjected to homogeneous quasistatic shearing. We show that these fluctuations share the following scaling characteristics of fluid turbulence in spite of their…
Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing…
We present a semi-Lagrangian scheme for the approximation of a class of Hamilton-Jacobi-Bellman equations on networks. The scheme is explicit and stable under some technical conditions. We prove a convergence theorem and some error…
In a series of papers, Bamler [Bam20a,Bam20b,Bam20c] further developed the high-dimensional theory of Hamilton's Ricci flow to include new monotonicity formulas, a completely general compactness theorem, and a long-sought partial regularity…
We consider the dynamics of an expanding superfluid modeled by Mueller-Israel-Stewart theory coupled to a complex scalar field with a $U(1)$ symmetry that is spontaneously broken. This is a manageable theoretical setting for explorations of…
We report and analyze the results of numerical studies of dense granular flows in two and three dimensions, using both linear damped springs and Hertzian force laws between particles. Chute flow generically produces a constant density…
In this study we give a characterization of semi-geostrophic turbulence by performing freely decaying simulations for the case of constant uniform potential vorticity, a set of equations known as surface semi-geostrophic approximation. The…
We theoretically and numerically investigate the steady flow of two-dimensional granular materials in a rotating drum using the discrete element method and a continuum model with the $\mu(I)$-rheology. The velocity fields obtained from both…
Wind-driven flow in power-law viscous fluids in homogeneous semienclosed basins is analyzed. Analytical solutions for vertical current profiles for non-newtonian fluids with different power-law indexes are derived assuming a wind shear…
The paper addresses the numerical approximation of two variants of hyperbolic mean curvature flow of surfaces in $\mathbb R^3$. For each evolution law we propose both a finite element method, as well as a finite difference scheme in the…
The article describes various aspects of mathematical modeling of fluid flows, both in general and with reference to hydraulic machinery. The article reviews historical development of corresponding methods of mathematical modeling.…
We systematically validate the static local mesh refinement capabilities of a recently proposed IMEX-DG scheme implemented in the framework of the deal.II library. Non-conforming meshes are employed in atmospheric flow simulations to…
The addition of suitable volume forces to the Navier-Stokes equation allows to simulate flows in the presence of a homogeneous shear. Because of the explicit form of the driving the flows are accessible to rigorous mathematical treatment…
We show that the clustering coefficient, a standard measure in network theory, when applied to flow networks, i.e. graph representations of fluid flows in which links between nodes represent fluid transport between spatial regions,…
We perform kinetic Monte Carlo simulations of flow-induced nucleation in polymer melts with an algorithm that is tractable even at low undercooling. The configuration of the non-crystallized chains under flow is computed with a recent…
We introduce a class of high order accurate, semi-implicit Runge-Kutta schemes in the general setting of evolution equations that arise as gradient flow for a cost function, possibly with respect to an inner product that depends on the…
Observations of the flow on Jupiter exists essentially only for the cloud-level, which is dominated by strong east-west jet-streams. These have been suggested to result from dynamics in a superficial thin weather-layer, or alternatively be…
While significant research has been dedicated to the simulation of fluids, not much attention has been given to exploring new interesting behavior that can be generated with the different types of non-Newtonian fluids with non-constant…
Saturation overshoot and pressure overshoot are studied by incorporating dynamic capillary pressure, capillary pressure hysteresis and hysteretic dynamic coefficient with a traditional fractional flow equation in one dimension. Using the…