Projections onto the Cone of Optimal Transport Maps and Compressible Fluid Flows

Three-dimensional characteristic approach for incompressible thermo-flows and influence of artificial compressibility parameter

In this paper the characteristics of unsteady three-dimensional incompressible flows with heat transfer are obtained along with artificial compressibility of Chorin. At first, compatibility equations and pseudo characteristics for three-dimensional flows are derived from five governing equations (continuity equation, Momentum equations in three directions, and energy equation) and then results ...

Model Reduction for Compressible Flows using POD and Galerkin Projection

We present a framework for applying the method of Proper Orthogonal Decomposition (POD) and Galerkin projection to compressible fluids. For incompressible flows, only the kinematic variables are important, and the techniques are well known. In a compressible flow, both the kinematic and thermodynamic variables are dynamically important, and must be included in the configuration space. We introd...

A Two -Step Modification toward Implementing Compressible Source Terms in Low Compressible Flows

Sticky Particle Dynamics with Interactions

We consider compressible pressureless fluid flows in Lagrangian coordinates in one space dimension. We assume that the fluid self-interacts through a force field generated by the fluid itself. We explain how this flow can be described by a differential inclusion on the space of transport maps, in particular when a sticky particle dynamics is assumed. We study a discrete particle approximation a...

Model Error in Filtering Random Compressible Flows Utilizing Noisy

Lagrangian tracers are drifters and floaters that collect real-time information of fluid flows. This paper studies the model error in filtering multiscale random rotating compressible flow fields utilizing noisy Lagrangian tracers. The random flow fields are defined through random amplitudes of Fourier eigenmodes of the rotating shallow water equations that contain both incompressible geostroph...