Flow Problems Research Articles

Optimizing pathfinding for goal legibility and recognition in cooperative partially observable environments

In this paper, we perform a joint design of goal legibility and recognition in a cooperative, multi-agent pathfinding setting with partial observability. More specifically, we consider a set of identical agents (the actors) that move in an environment only partially observable to an observer in the loop. The actors are tasked with reaching a set of locations that need to be serviced in a timely fashion. The observer monitors the actors' behavior from a distance and needs to identify each actor's destination based on the actor's observable movements. Our approach generates legible paths for the actors; namely, it constructs one path from the origin to each destination so that these paths overlap as little as possible while satisfying budget constraints. It also equips the observer with a goal-recognition mapping between unique sequences of observations and destinations, ensuring that the observer can infer an actor's destination by making the minimum number of observations (legibility delay). Our method substantially extends previous work, which is limited to an observer with full observability, showing that optimizing pathfinding for goal legibility and recognition can be performed via a reformulation into a classical minimum cost flow problem in the partially observable case when the algorithms for the fully observable case are appropriately modified. Our empirical evaluation shows that our techniques are as effective in partially observable settings as in fully observable ones.

Analysis of free convective flow of nanofluid due to inclined surface with thermos-diffusion effects and chemical reaction

An unsteady free convective flow of nanofluid is studied due to inclined surface in presence of thermos-diffusion effects. The chemical reaction, radiative phenomenon and heat source features are also utilized to discuss the transport phenomenon. The properties of nanomaterials are endorsed with interaction of copper, titanium oxide and aluminum oxide nanoparticles. The dimensionless system is achieved for the governing model. The analysis solution with perturbation technique is suggested. The illustration of thermal flow problem is visualized with variation of parameters graphically. The numerical outcomes are also computed and illustrated.

Experimental and numerical investigation of shelf flow crossing over a strait

Motivated by the phenomenon of Scotian Shelf Crossover events, the problem of a shelf flow that is interrupted by a strait is considered. Laboratory experiments in a rotating tank with barotropic and baroclinic flow over flat and sloping shelves confirm that the flow is steered by the bathymetric contours and mainly circumnavigates the gulf. In order to jump across the strait, as suggested by earlier theories, the flow must have unrealistically high Rossby numbers. However, the near bottom friction relaxes the bathymetric constraint and causes the formation of a peculiar jet crossing the strait diagonally. For the dissipation values such that a half of the transport goes around the gulf and half crosses the strait diagonally, the diagonal crossover jet becomes most evident. Numerical solutions for realistic values of the frictional parameter reproduce the results of the laboratory experiments and consideration of the actual Gulf of Maine bathymetry reproduces patterns similar to those observed by drift trajectories and in the satellite derived sea surface temperature fields.

The Maximum Attainable Flow and Minimal Cost Problem in a Network

This paper, presents an efficient algorithm that solves such a large class of optimization problems. Ford-Fulkerson determines the maximum flow in a network by iteratively augmenting flow paths until no further improvement is possible. On the other hand, Dijkstra's algorithm excels in finding the shortest path in a weighted graph, making it suitable for minimizing costs in network traversal. However, this paper simultaneously optimizes both objectives (flow and cost) dependently in unique iterations by considering all constraints and objectives holistically. The aim of this work is to develop efficient algorithms that can handle complex optimization problems in transportation, network design, and other fields, ultimately improving resource utilization and minimizing costs as its crucial for enhancing decision-making processes, improving efficiency in resource utilization, and achieving cost savings in diverse applications ranging from transportation networks to production planning. This paper deals about formulating the linear programming for the optimizations problems and finding the maximum amount of flow that can be sent from a source node to a sink node while minimizing the total cost of sending that flow by using simplex method (Two phase method). Through computational experiments and case studies, everybody demonstrate the effectiveness and efficiency of the proposed approach in solving real-world network flow problems. Our method yields efficient algorithms with in smallest numbers of iterations and time that enable the optimal allocation of resources within networks, achieving both maximum flow and minimum cost simultaneously.

Surface tension and wetting at free surfaces in smoothed particle hydrodynamics

Surface tension and wetting are dominating physical effects in microscale and nanoscale flows. We present an efficient and reliable model of surface tension and equilibrium contact angles in smoothed particle hydrodynamics for free-surface problems. We demonstrate its robustness and accuracy by simulating several three-dimensional free-surface flow problems driven by interfacial tension.

A systematic analysis of three-dimensional Riemann problems for verification of compressible-flow solvers

Numerical simulation is a well-established way of analyzing compressible flows. Due to high computational demands of solvers for such flow problems, their verification is typically limited to two-dimensional (2D) cases. However, 2D simulations suppress fundamental three-dimensional (3D) aspects of the flow evolution in (compressible) turbulent flows or shock-bubble and shock-drop interactions. With increase of computational power, 3D simulations become more feasible for routine analyses. The verification of 3D simulation frameworks is often limited to transformations of lower dimensional test cases in the 3D space. There is a lack of strictly 3D reference test cases for gas dynamics. In this work, we present a set of genuine 3D Riemann problems in order to validate and verify numerical solvers for compressible flows. The problems are designed such that each octant’s constant initial data connects two neighboring states by an elementary wave only. The problem design is inspired by well-established 2D Riemann problems most prominently posted by Lax and Liu (1998). In contrast to the twenty published 2D cases, more than 300 distinct combinations can be found in 3D. We provide example solutions for the particularly interesting ones of these case combinations and show how the cases help to expose shortcomings of numerical solvers. We provide reference data from computations with an open-source compressible multiresolution flow solver. For the reference solutions, we employ the Harten-Lax-van Leer contact (HLLC) Riemann solver and a weighted essentially non-oscillatory (WENO) reconstruction stencil of fifth order. The reference solutions use an effective resolution of one billion cells. We additionally make the full compute pipeline of this work publicly available, so interested researchers may reproduce and extend the current work.

A sharp-interface level-set formalism for multiphase suspension flows

The present paper addresses the problem of multiphase incompressible suspension flows where an interface with a gas phase is explicitly taken into account in a sharp manner. We define the suspension phase as a mixture of a liquid and non-colloidal particles and a level-set method is used to track the position of the interface between the suspension and the gas phase. The presence of particles in the liquid phase is accounted for in an Euler-Euler manner: properties of the suspension vary locally with the particle volume fraction which is accurately resolved with the use of high-order schemes. Since two-phase flows are considered, specific attention is given to the interface region in order to limit spurious forces and mass loss. The overall method turns out to be robust and accurately captures complex suspension flows as illustrated by selected results.

Implementation and Validation of an Original OpenFOAM Code for Fluid–Structure Interaction Problems in Compressible Flow

Implementation and Validation of an Original OpenFOAM Code for Fluid–Structure Interaction Problems in Compressible Flow

Robust reverse 1-center problems on trees with interval costs

This paper concerns the problem of reducing the edge lengths of a tree in a minimum cost way such that the 1-center function at a predetermined vertex is at most a given threshold value. Moreover, it is assumed that the costs of reducing edge lengths are not exactly determined, but they are estimated within intervals and their total deviation is limited within a given bound. This problem is called the robust reverse 1-center problem on trees with interval costs. We first reformulate the problem as a Stackelberg game and translate it into a univariate optimization problem. Based on the special properties of the feasible set, we can state the corresponding problem as a parameterized minimum cost flow problem. Then we develop an algorithm that solves the problem in O ( n 2 log ⁡ n ) time due to the convexity of the univariate objective function. We finally discuss the problem of improving the international transportation network in Iran as a real-life application.

Cellulose Nanofiber/Polyethylene Glycol Composite Phase Change Thermal Storage Gel Based on Solid-gel Phase Change

In this paper, cellulose nanofiber (CNF)/ polyethylene glycol (PEG) composite aerogel phase change materials (CNPCMs) were prepared utilizing porous carrier support and freeze-drying. The solid-liquid phase change to solid-gel phase change was realized, which solved the problems of PEG flow, leakage, and shape instability. The physical properties and chemical compatibility of CNPCMs were studied, and the results showed that CNPCMs ensured the overall structure stability through internal hydrogen bonding, and they were only a physical bond with each other without chemical reaction. With the increase in PEG content, the thermal conductivity of CNPCMs increased from 0.22 W/m·K to 0.33 W/m·K. The thermal exposure experiment and thermogravimetric analysis (TGA) experiment have shown that CNPCMs have good shape stability at 75 ℃ and good thermal stability below 320 ℃. In summary, the experimental results indicated that the maximum content of PEG in CNPCMs was 78 % with an optimal content of 66.7 %. The sample corresponding to the optimal content was CNPCM2 with an enthalpy of 167.9 J/g for melting and 146.1 J/g for solidification. As a thermal storage material with good thermodynamic performance, CNPCM2 has enormous potential in the storage of solar collectors.

Optimal convergence analysis of two RPC-SAV schemes for the unsteady incompressible magnetohydrodynamics equations

Abstract In this paper, we present and analyze two linear and fully decoupled schemes for solving the unsteady incompressible magnetohydrodynamics equations. The rotational pressure-correction (RPC) approach is adopted to decouple the system, and the recently developed scalar auxiliary variable (SAV) method is used to treat the nonlinear terms explicitly and keep energy stability. One is the first-order RPC-SAV-Euler and the other one is generalized Crank–Nicolson-type scheme: GRPC-SAV-CN. For the RPC-SAV-Euler scheme, both unconditionally energy stability and optimal convergence are derived. The new GRPC-SAV-CN is constructed and can be regarded as a parameterized scheme, which includes PC-SAV-CN when the parameter $\beta =0$ and RPC-SAV-CN when $\beta \in (0,\frac {1}{2}]$; see Algorithm 3.2. However, Jiang and Yang (Jiang, N. & Yang, H. (2021) SIAM J. Sci. Comput., 43, A2869–A2896) point out that the SAV method has low accuracy by several commonly tested benchmark flow problem when solving Navier–Stokes equations. To improve the accuracy, we added two stabilization $-\alpha _{1}\varDelta t\nu \varDelta (\widetilde {\textbf {u}}^{n+1}-{\textbf {u}}^{n})$ and $\alpha _{2}\varDelta t\sigma ^{-1}\mbox {curl}\mbox {curl} (\textbf {H}^{n+1}-\textbf {H}^{n})$ in the GRPC-SAV-CN scheme, which play decisive roles in giving optimal error estimates. The unconditionally energy stability of the proposed scheme is given. We prove that the PC-SAV-CN scheme has second-order convergence speed, and the RPC-SAV-CN one has 1.5-order convergence rate. Finally, some numerical examples are presented to verify the validity and convergence of the numerical schemes.

A comparison study of spatial and temporal schemes for flow and transport problems in fractured media with large parameter contrasts on small length scales

AbstractIn this work, various high-accuracy numerical schemes for transport problems in fractured media are further developed and compared. Specifically, to capture sharp gradients and abrupt changes in time, schemes with low order of accuracy are not always sufficient. To this end, discontinuous Galerkin up to order two, Streamline Upwind Petrov-Galerkin, and finite differences, are formulated. The resulting schemes are solved with sparse direct numerical solvers. Moreover, time discontinuous Galerkin methods of order one and two are solved monolithically and in a decoupled fashion, respectively, employing finite elements in space on locally refined meshes. Our algorithmic developments are substantiated with one regular fracture network and several further configurations in fractured media with large parameter contrasts on small length scales. Therein, the evaluation of the numerical schemes and implementations focuses on three key aspects, namely accuracy, monotonicity, and computational costs.

Graph‐based solution for smart grid real‐time operation and control

Graph‐based solution for smart grid real‐time operation and control

Numerical approximations of groundwater flow problem using fractional variational iteration method with fractional derivative of singular and nonsingular kernels

This study aims to present the numerical approximations of groundwater flow problem, namely the time-fractional Boussinesq equation using the fractional variational iteration method. Fractional derivatives in time variable are taken in Caputo and Caputo–Fabrizio sense. This work compares the solutions of the time-fractional Boussinesq equation for the Caputo and Caputo–Fabrizio fractional operators. Graphical representation of the water table head’s behavior for different time values is shown.

Analytical and numerical study of water-based silver nanofluid (Ag) across a Riga plate with nonlinear radiation and viscous dissipation: A three-dimensional study

The primary endeavor of this investigation is to determine the Darcy–Forchheimer flow of water-based silver nanofluid (Ag) across a bidirectional Riga plate with viscous dissipation and nonlinear radiation. By manipulating the pertinent variables, the governing equations undergo a transformation into nonlinear ordinary differential equations. The remodeled flow problems are investigated numerically and analytically using the MATLAB (bvp4c built-in function) algorithm and the homotopy analysis method scheme. The repercussions of the appropriate factors on the x− and y− direction velocity profiles, temperature profile, skin friction coefficient of the x− and y− directions, and local Nusselt number are examined via tables and graphs. It is found that both directional fluid velocities decline in the presence of the suction/injection parameter. Increasing the radiation parameter and the Eckert number exalts the fluid temperature. The surface shear stress decays as the suction/injection parameter and the Forchheimer number grow larger. In addition, a greater heat transfer rate appears on the Riga plate compared to the stationary plate.

Heat and concentration analysis of two-layered muco-ciliary third grade fluid flow in human airways

Understanding the mechanisms involved in the movement and clearance of mucus within the human airways is important from a physiological perspective. A mathematical model of muco-ciliary two-layered fluid flow in a finite two-dimensional channel is proposed. Due to the presence of both the airway ciliary layer (ACL) and the periciliary liquid layer (PCL) in airways epithelial cells, the two-layered model is adopted. The third grade fluid models is used to characterize the viscoelastic nature of mucus secreted in the airways. The mathematical modeling of two-layer flow problem is simplified by using long wavelength and small Reynolds number approximation. A formulated set of partial differential equations (PDEs) is solved for series-form solutions of velocity, temperature, concentration, and pressure gradient by using the Adomian decomposition method (ADM). The analysis delineated that with an increase in pressure gradient at airways entrance ξ the velocity and temperature increases while concentration decreases. Deborah numbers impact ACL and PCL velocities differently, with De(A) influencing flow direction and De(P) causing fluid to flow faster in the forward direction. It also emphasizes the significance of the rate of thermal diffusion, viscous dissipation, and relaxation time. The results showed that the suggested two-layered muco-ciliary model provides a better description of mucus transport in the human airways. The pressure gradient at the airways entrance has a significant impact on mucus transport through the airways.

Distributionally robust disaster relief planning under the Wasserstein set

We study a two-stage natural disaster management problem modeled as a stochastic program, where the first stage consists of a facility location problem, deciding where to open facilities and pre-allocate resources such as medical and food kits, and the second stage is a fixed-charge transportation problem, routing resources to affected areas after observing a disaster. Our model has binary variables present in both stages. Due to the lack of data, classical stochastic programming approaches may be ill-suited, and we propose a two-stage distributionally robust formulation with a Wasserstein ambiguity set, where we consider distributions consistent with historical data and a tunable parameter to control the level of risk aversion. We develop a tailored column-and-constraint generation (CCG) algorithm to solve an extensive reformulation, where scenarios are iteratively generated. We handle the presence of binary variables in the second stage by leveraging the structure of our support set and second-stage problem, and provide conditions under which the optimal value of the latter is concave with respect to the intensity of the disaster, leading to an efficient scenario generation procedure. We also show that our results extend to the case where the second stage is a fixed-charge network flow problem. We perform extensive computational experiments demonstrating the computational advantage of our method over classical CCG implementations on synthetic instances, and illustrate the benefits of our approach on a popular case study from the literature of hurricane threats on the Gulf of Mexico in the United States.

A modified cell-centered nodal integral scheme for the convection-diffusion equation

The nodal integral methods (NIMs) are very efficient and accurate coarse-mesh methods for solving partial differential equations. The cell-centered NIM (CCNIM) is a simplified variant of the NIMs that has recently shown its efficiency in solving fluid flow problems but has been hampered by issues such as inapplicability to one-dimensional problems, complexities in handling Neumann boundary conditions and the formulation of a system of differential-algebraic equations (DAEs) for discrete unknowns. Here, we present a modified version of the CCNIM designed to overcome the challenges associated with its previous version. Our novel development retains the essence of CCNIM while resolving these issues. The proposed scheme, grounded in the nodal framework, achieves second-order accuracy in both spatial and temporal dimensions. Unlike its precursor, the proposed method formulates algebraic equations for discrete variables per node, eliminating the cumbersome DAE system. Neumann boundary conditions are seamlessly incorporated through a straightforward flux definition, and applicability to one-dimensional problems is now feasible. We successfully apply our approach to one and two-dimensional convection-diffusion problems with known analytical solutions to validate our approach. The simplicity and robustness of the approach lay the foundation for its seamless extension to more complex fluid flow problems.

Distributed Physics-Informed machine learning strategies for two-phase flows

This study delves into applying Distributed Learning Machines (DLM), a subset of Physics-Informed Neural Networks (PINN), in tackling benchmark challenges within two-phase flows. Specifically, two variants of DLM, namely Distributed Physics-Informed Neural Networks (DPINN) and Transfer Physics-Informed Neural Networks (TPINN), are studied. The DLM architecture strategically divides the global domain into distinct non-overlapping sub-domains, with interconnected solutions facilitated by interface conditions embedded in the loss function. Forward and inverse benchmark problems in two-phase flows are explored: (a) bubble in a reversing vortex and (b) Bubble Rising under Buoyancy. The Volume of Fluid (VOF) method handles interface transport in both scenarios, with the inverse problem incorporating interface-position data during the training phase. The forward problem highlights the effectiveness of DPINN in capturing the interface using a simple transport equation. The distinctive contribution of this work lies in its exploration of the inverse problem, offering insights into the scalability of distributed architectures when dealing with a system of governing equations. Following the validation of an initial PINN model against Computational Fluid Dynamics (CFD) data, the study extends to DPINN and TPINN. A parametric study optimizes network hyperparameters, emphasizing the regularization of loss terms within the DPINN loss function. A self-adaptive weighting strategy based on a Gaussian probabilistic model dynamically adjusts loss weights during training to overcome challenges associated with manual parameter tuning. The evaluation of accuracy against CFD data and published results underscore the efficacy of DLMs in addressing two-phase flow problems. Additionally, the computational efficiency of distributed networks is explored compared to traditional PINNs.

Second-order, positive, and unconditional energy dissipative scheme for modified Poisson–Nernst–Planck equations

First-order energy dissipative schemes in time are available in literature for the Poisson–Nernst–Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite volume discretization in space for modified PNP equations that incorporate effects arising from ionic steric interactions and dielectric inhomogeneity. A multislope method on unstructured meshes is proposed to reconstruct positive, accurate approximations of mobilities on faces of control volumes. Numerical analysis proves that the proposed numerical schemes are able to unconditionally ensure the existence of positive numerical solutions, original energy dissipation, mass conservation, and preservation of steady states at discrete level. Extensive numerical simulations are conducted to demonstrate numerical accuracy and performance in preserving properties of physical significance. Applications in ion permeation through a 3D nanopore show that the modified PNP model, equipped with the proposed schemes, has promising applications in the investigation of ion selectivity and rectification. The proposed second-order discretization can be extended to design temporal second-order schemes with original energy dissipation for a type of gradient flow problems with entropy.