Related papers: Optimal profiles in variable speed flows
In this work a simple problem on 2D optimal shape for body immersed in a viscous flow is analyzed. The body has geometrical constraints and its profile would be found in the class of cubics which satisfy those conditions. The optimal…
A nonlinear differential equation about optimal shapes for blades of a fan. A boundary value differential problem from engineering, geometrical or physical bonds. A relation between linear profiles and constant speed along the side under…
Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…
We obtain a complete solution to the problem of classifying all two-dimensional ideal fluid flows with harmonic Lagrangian labelling maps; thus, we explicitly provide all solutions, with the specified structural property, to the…
In the optimal velocity model with a time lag, we show that there appear multiple exact solutions in some ranges of car density, describing a uniform flow, a stable and an unstable congested flows. This establishes the presence of…
Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
In this paper, we introduce the solver ConvexFlows for the convex flow problem first defined in the authors' previous work. In this problem, we aim to optimize a concave utility function depending on the flows over a graph. However, unlike…
A model for the development of turbulent shear flows, created by non-uniform parallel flows in a confining channel, is used to identify the diffuser shape that maximises pressure recovery when the inflow is non-uniform. Wide diffuser angles…
An obstacle is immersed in an externally driven 2D Stokes or Navier-Stokes fluid. We study the self-equilibration conditions for that obstacle under steady state assumptions on the flow. We then seek to optimize the translational and/or…
We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…
This article provides a computational evaluation of the popular high resolution upwind WACEB, CUBISTA and ADBQUICKEST schemes for solving non-linear fluid dynamics problems. By using the finite difference methodology, the schemes are…
We define a new notion of translations in the hyperbolic plane and explicitly solve the equation of the curve shortening flow. Next, we consider the class of ancient convex solutions and solve the equation of the curve shortening flow when…
To generate safe and real-time trajectories for an autonomous vehicle in dynamic environments, path and speed decoupled planning methods are often considered. This paper studies speed planning, which mainly deals with dynamic obstacle…
The Alternating Current Optimal Power Flow (ACOPF) problem remains one of the most fundamental yet computationally challenging tasks in power systems operation and planning due to its nonconvex, nonlinear, and multimodal nature. This paper…
We study a 2D potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular solution of Euler equations having a pair of square-root branch points…
Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The Navier-Stokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601x601. The steady…
Exploring the general analytical solutions to the Euler equations for ideal fluids holds significant theoretical and practical importance. The steady flows in two-dimensional spaces are considered whether there is an analytical solution in…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
A 2-D version of the asymmetric exclusion model for granular sheared flows is presented. The velocity profile exhibits two qualitatively different behaviors, dependent on control parameters. For low friction, the velocity profile follows an…