Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that addressed here with a continuous model relying on optimal transport theory. A physics informed neuralnetwork method advocated for the solution corresponding generalized Monge-Amp`ere equation. Convex neural networks are enforce convexity Monge-Amp\`ere equation and obtain suitable approximation map. particular focus set enforcement boundary conditions loss function. Numerical experiments...

We address in this article the computation of convex solutions Dirichlet problem for real elliptic Monge-Ampère equation general domains two dimensions.The method we discuss combines a least-squares formulation with relaxation method.This approach leads to sequence Poisson-Dirichlet problems and another low dimensional algebraic eigenvalue new type.Mixed finite element approximations smoothing procedure are used computer implementation our least-squares/relaxation methodology.Domains curved...

Abstract. A variety of thermodynamic models have been developed to predict inorganic gas-aerosol equilibrium. To achieve computational efficiency a number the rely on priori specification phases present in certain relative humidity regimes. Presented here is new model, named UHAERO, that both efficient and rigorously computes phase behavior without any specification. The implementation based minimization Gibbs free energy using primal-dual method, coupled Newton iteration. mathematical...

We present a multi-physics model for the approximation of coupled system formed by heat equation and Navier-Stokes equations with solidification free surfaces. The computational domain is union two overlapping regions: larger to account thermal effects, smaller region fluid flow. Temperature-dependent surface effects are accounted via tension Marangoni forces. volume-of-fluid approach used track surfaces between metal (liquid or solidified) ambient air. numerical method incorporates all...

In this article, we address the numerical solution of a non-smooth eigenvalue problem, which has implications in plasticity theory and image processing. The smallest operator under consideration is shown to be same for all bounded, sufficiently smooth, domains two space dimensions. Piecewise linear finite elements are used discretization eigenfunctions eigenvalues. An augmented Lagrangian method proposed computation minima associated non-convex optimization problem. convergence element...

Ordinary differential equations are coupled with mixed constrained optimization problems when modeling the thermodynamic equilibrium of a system evolving time. A particular application arises in atmospheric particles. Discontinuity points created by activation/deactivation inequality constraints. numerical method for solution optimization-constrained is proposed coupling an implicit Runge–Kutta (RADAU5), techniques detection events (activation and deactivation constraints). The computation...

In this article, we address the numerical solution of Dirichlet problem for three-dimensional elliptic Monge–Ampère equation using a least-squares/relaxation approach. The relaxation algorithm allows decoupling differential operators from nonlinearities. Dedicated solvers are derived efficient local optimization problems with cubicly nonlinear equality constraints. approximation relies on mixed low order finite element methods regularization techniques. results experiments show convergence...

Abstract. In atmospheric aerosols, water and volatile inorganic organic species are distributed between the gas aerosol phases in accordance with thermodynamic equilibrium. Within an particle, liquid solid can exist at Models for computation of phase equilibria inorganic/water mixtures typical aerosols; when present, equilibrium problem is complicated by organic/water interactions as well potentially large number species. We present here extension UHAERO model (Amundson et al., 2006c) to...

Computation of phase and chemical equilibria water‐organic‐inorganic mixtures is significant interest in atmospheric aerosol modeling. A new version the partitioning model, named UHAERO, presented here, which allows one to compute behavior for aerosols containing inorganic electrolytes organic compounds. The computational implementation model based on standard minimization Gibbs free energy using a primal‐dual method, coupled Newton iteration. Water uptake deliquescence properties aqueous...

In this article, we discuss the numerical solution of a constrained minimization problem arising from stress analysis elasto-plastic bodies.This has flavor generalized non-smooth eigenvalue problem, with smallest corresponding to load capacity ratio elastic body under consideration.An augmented Lagrangian method, together finite element approximations, is proposed for computation optimum objective function, and minimizer.The approach allows decoupling some nonlinearities differential...

We present a numerical model for the simulation of 3D poly-dispersed sediment transport in Newtonian flow with free surfaces. The physical is based on mixture multiphase flows. Navier–Stokes equations are coupled and deposition particle concentrations, volume-of-fluid approach to track surface between water air. algorithm relies operator-splitting decouple advection diffusion phenomena. Two grids used, unstructured finite elements an appropriate combination characteristics method Godunov's...

SUMMARY A numerical method for the solution to density‐dependent incompressible Navier–Stokes equations modeling flow of N immiscible liquid phases with a free surface is proposed. It allows model an arbitrary number together additional vacuum phase separated surface. based on volume‐of‐fluid approach involving indicator functions (one per phase, identified by its density) that guarantees mass conservation within each phase. An function whole domain treat boundary conditions at interface...