Solution Of Flow Problems Research Articles

A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems

A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems

Development of an optimal adaptive finite element stabiliser for the simulation of complex flows

An optimal adaptive multiscale finite element method(AMsFEM) for numerical solutions of flow problems modelled by the Oldroyd B model is developed. Complex flows experience instabilities due to a phenomena known as the high Weissenberg number problem. The stabilisers are terms in-cooperated into the variational formulation when applying the finite element method. For the selected few stabilisers, numerical experiments are performed to study the convergence of the solutions. These demonstrate that adaptive strategies reduce the computational load of flow simulation. A best performing combination of choice of stabiliser and adaptive strategy is suggested.

Effect of Graded Mesh Number on the Solution of Convection-Diffusion Flow Problem with Quadratic Source

Convection-diffusion phenomena are fundamentally modelled in a variety of engineering fields and physical sciences. A suitable meshing strategy is needed in computational fluid dynamics to solve model problems numerically. Unintentional implementation of the approach could lead to subpar solutions such as erroneous oscillations, over- or under-predictions, and excessive computing time. This paper highlights the significance of the influence of mesh structure on the solution of convection-diffusion flow problem with quadratic source for flow parameters of interest. Particularly, it presents the accuracy of the solution of the flow problem at low Peclet number with respect to graded mesh number, where the expansion factor used is based on an established linear logarithmic model involving Peclet number derived in previous works. The problem is solved by assigning several mesh intervals to graded mesh against each Peclet number of interest. Based on the values of the interval and Peclet number, 16 test cases are considered. Quantitative results lead to orders of accuracy of the solution of the flow problem. The effect of graded mesh number on the accuracy thus serves as a reference for a more structured decision-making and improves the heuristic process in choosing the computational domain mesh with expected order of accuracy for the numerical solution of the problem particularly in the calculation of scalar concentration. The orders of accuracy confirm the profiles of concentration.

Asymptotic Solutions of Flow Problems with Boundary Layer of Double-Deck Structures

Asymptotic Solutions of Flow Problems with Boundary Layer of Double-Deck Structures

Energy flow problem solution based on state estimation approaches and smart meter data

Accurate electric energy (EE) measurements and billing estimations in a power system necessitate the development of an energy flow distribution model. This paper summarizes the results of investigations on a new problem related to the determination of EE flow in a power system over time intervals ranging from minutes to years. The problem is referred to as the energy flow problem (EFP). Generally, the grid state and topology may fluctuate over time. An attempt to use instantaneous (not integral) power values obtained from telemetry to solve classical electrical engineering equations leads to significant modeling errors, particularly with topology changes. A promoted EFP model may be suitable in the presence of such topological and state changes. Herein, EE flows are determined using state estimation approaches based on direct EE measurement data in Watt-hours (Volt-ampere reactive-hours) provided by electricity meters. The EFP solution is essential for a broad set of applications, including meter data validation, zero unbalance EE billing, and nontechnical EE loss check.

A Robust Pseudo-Three-Dimensional Computational Fluid Dynamic Approach for Industrial Applications

Abstract Two-dimensional instead of three-dimensional computational fluid dynamic solutions of flow problems are quite often used in industry to facilitate short design turn-around times with varying degrees of success. A simple and robust approach for improving the accuracy of two-dimensional computational fluid dynamics solutions for problems involving internal flow passages in industrial applications is presented. The technique utilizes an approximation to the shearing stresses that act in the fully three-dimensional case but are ignored in the traditional two-dimensional approximation. Although the technique does not fully account for all the three-dimensional effects in such flows, it gives a reasonable estimate of the operation of devices with internal flows, even those involving transients. The usefulness and accuracy of the method are demonstrated through the application of the method to predict the performance of a supersonic fluidic oscillator for industrial design purposes. This brief provides industrial designers with a simple and robust tool for improving the accuracy of their computational fluid dynamic simulations.

3D modeling of generalized Newtonian fluid flow with data assimilation using the least-squares finite element method

In this contribution we present a least-squares finite element formulation to model steady-state flow of incompressible, non-Newtonian fluids in three dimensions including data assimilation. The approach is based on the incompressible Navier–Stokes equations and the nonlinear viscosity is considered by means of the Carreau–Yasuda viscosity model, which can account for shear-thickening and shear-thinning behavior of generalized Newtonian fluids. We outline the procedure how to integrate given data into the numerical solution of flow problems without additional computational cost using the least-squares FEM. Assimilation of experimental data provides the opportunity to reduce model errors resulting in a solution which more closely approximates reality. Furthermore, the preprocessing of the available data using Kriging interpolation is also described briefly.The presented formulation is first validated by investigating the flow in a cube with an exact solution without data assimilation. Convergence is evaluated based on the error in velocities and pressure compared to the exact solution. Then the effect of data assimilation is shown by modeling blood flow through a carotid bifurcation model and integrating data either along lines or over entire cross-sectional areas. The improvement of the numerical solution by means of data assimilation is revealed by comparing the calculated velocity profiles with experimental and numerical reference values.

Asymptotic Solutions of Flow Problems with Boundary Layer of Double-Deck Structures

В работе излагается общая схема построения многомасштабных асимптотических решений, возникающих в задачах обтекания поверхности с малыми неровностями. Уточняются результаты известных работ по гидродинамике. Библиография: 25 названий.

A high-order implicit least square-based finite difference-finite volume method for incompressible flows on unstructured grids

In this study, a high-order implicit least squares-based finite difference-finite volume (ILSFD-FV) method with a lattice Boltzmann flux solver is presented for the simulation of two-dimensional incompressible flows on unstructured grids. In this method, a high-order polynomial based on Taylor series expansion is applied within each control cell, where the unknown spatial derivatives at each cell center are approximated by the least squares-based finite difference scheme. The volume integral of the high-order polynomial over the control cell results in a pre-multiplied coefficient matrix in the time-dependent term. This makes the high-order method be implicit in nature. With this feature, a high-order implicit Runge–Kutta time integration scheme, namely, the explicit first-stage singly diagonally implicit Runge–Kutta (ESDIRK) scheme, is applied to obtain the time-accurate solutions for flow problems. The non-linear system of equations arising from each ESDIRK stage except for the first explicit stage is solved by a dual time stepping approach. A matrix-free lower-upper symmetric Gauss–Seidel solver is then used to efficiently march the solution in the pseudo time. The present high-order ILSFD-FV method is verified and validated by both steady and unsteady 2D incompressible flow problems. Numerical results indicate that the developed implicit method outperforms its explicit counterpart in terms of the convergence property and computational efficiency. The speedup ratio of the computational effort is about 3–22.

Security Constrained Optimal Power Flow Problem Solution with Practical Constraints using HALOA

To solve the OPF problems with three objective functions like fuel cost minimization, emission and power loss. The proposed algorithm is hybridizing conventional Anti Lion optimization algorithm with Genetic algorithm. The considered objectives are solved by considering the equality and in-equality constraints along with practical constraints. The effectiveness of the proposed method is tested on the IEEE 30 bus test system and compared with existing literature. The proposed method gives the best optimal values for the minimizing the considered objectives.

Geometric multigrid methods for Darcy–Forchheimer flow in fractured porous media

In this paper, we present a monolithic multigrid method for the efficient solution of flow problems in fractured porous media. Specifically, we consider a mixed-dimensional model which couples Darcy flow in the porous matrix with Forchheimer flow within the fractures. A suitable finite volume discretization permits to reduce the coupled problem to a system of nonlinear equations with a saddle point structure. In order to solve this system, we propose a full approximation scheme (FAS) multigrid solver that appropriately deals with the mixed-dimensional nature of the problem by using mixed-dimensional smoothing and inter-grid transfer operators. Numerical experiments show that the proposed multigrid method is robust with respect to the fracture permeability, the Forchheimer coefficient and the mesh size. The case of several possibly intersecting fractures in a heterogeneous porous medium is also discussed.

On new scaling group of transformation for Prandtl-Eyring fluid model with both heat and mass transfer

Abstract A short communication is structured to offer a set of scaling group of transformation for Prandtl-Eyring fluid flow yields by stretching flat porous surface. The fluid flow regime is carried with both heat and mass transfer characteristics. To seek solution of flow problem a set of scaling group of transformation is proposed by adopting Lie approach. These transformations are used to step down the partial differential equations into ordinary differential equations. The reduced system is solved by numerical method termed as shooting method. A self-coded algorithm is executed in this regard. The obtain results are elaborated by means of figures and tables.

Parallel anisotropic mesh refinement with dynamic load balancing for transonic flow simulations

Abstract The present paper discusses an effective adaptive methods suited for use in parallel environment. An in-house, parallel flow solver based on the residual distribution method is used for the solution of flow problems. Simulation is parallelized based on the domain decomposition approach. Adaptive changes to the mesh are achieved by two distinctive techniques. Mesh refinement is performed by dividing element edges and a subsequent application of pre defined splitting templates. Mesh regularization and derefinement is achieved through topology conserving node movement (r-adaptivity). Parallel implementations of an adaptive use the dynamic load balancing technique.

Performance assessment of iterative linear methods for the computation of the power flow problem solution

Performance assessment of iterative linear methods for the computation of the power flow problem solution

Comparison of discontinuous Galerkin time integration schemes for the solution of flow problems with deformable domains

The computational efficiency of numerical solvers is known to strongly depend on the chosen time integration scheme. Thus, when solving viscous flow problems on time-varying domains, an efficient and reliable solver is one of the prerequisites for a successful solution. For this reason, we provide a comparison of two time integration schemes in terms of numerical error and CPU time usage.The contribution of the paper lies in the mutual comparison of two different approaches for time integration of the compressible Navier–Stokes equations in arbitrary Lagrangian–Eulerian (ALE) description that are spatially discretised by the discontinuous Galerkin finite element method. The computational ability of implicit Crank–Nicolson scheme and explicit three-step Runge–Kutta scheme, computational performance of which is improved by the local time-stepping technique, are tested on two flow problems: the propagation of an isentropic vortex, which has a known analytical solution, and the viscous flow around an oscillating NACA 0012 airfoil. All numerical simulations are carried out on unstructured triangular meshes by using a continuous mapping between the reference and time-varying domains.

Directional Do-Nothing Condition for the Navier-Stokes Equations

The numerical solution of flow problems usually requires bounded domains although the physical problem may take place in an unbounded or substantially larger domain. In this case, artificial boundaries are necessary. A well established artificial boundary condition for the Navier-Stokes equations discretized by finite elements is the condition. The reason for this is the fact that this condition appears automatically in the variational formulation after partial integration of the viscous term and the pressure gradient. This condition is one of the most established outflow conditions for Navier-Stokes but there are very few analytical insight into this boundary condition. We address the question of existence and stability of weak solutions for the Navier-Stokes equations with a directional do-nothing condition. In contrast to the usual condition this boundary condition has enhanced stability properties. In the case of pure outflow, the condition is equivalent to the original one, whereas in the case of inflow a dissipative effect appears. We show existence of weak solutions and illustrate the effect of this boundary condition by computation of steady and non-steady flows.

Numerical Simulation of Multiphase Flows for Rubber Materials

In an extrusion process of rubber materials, there are a liquid-liquid phase and a gas-liquid phase. It is difficult to solve viscoelastic flow with high Weissenberg number. In this paper, interface between rubbers is solved by using the commercial software. The difficulty in the numerical simulation is specified. The solution to this problem is proposed. The proposed method is applied to the numerical solution of flow problems for a viscoelastic fluid in arbitrary computation domains. The proposed method is enabled to solve the viscoelastic flow with high Weissenberg number in comparison with the conventional method.

Multiscale modeling with smoothed dissipative particle dynamics

In this work, we consider two issues related to the use of Smoothed Dissipative Particle Dynamics (SDPD) as an intermediate mesoscale model in a multiscale scheme for solution of flow problems when there are local parts of a macroscopic domain that require molecular resolution. The first is to demonstrate that SDPD with different levels of resolution can accurately represent the fluid properties from the continuum scale all the way to the molecular scale. Specifically, while the thermodynamic quantities such as temperature, pressure, and average density remain scale-invariant, we demonstrate that the dynamic properties are quantitatively consistent with an all-atom Lennard-Jones reference system when the SDPD resolution approaches the atomistic scale. This supports the idea that SDPD can serve as a natural bridge between molecular and continuum descriptions. In the second part, a simple multiscale methodology is proposed within the SDPD framework that allows several levels of resolution within a single domain. Each particle is characterized by a unique physical length scale called the smoothing length, which is inversely related to the local number density and can change on-the-fly. This multiscale methodology is shown to accurately reproduce fluid properties for the simple problem of steady and transient shear flow.

Monotonic solution of flow and transport problems in heterogeneous media using Delaunay unstructured triangular meshes

Transport problems occurring in porous media and including convection, diffusion and chemical reactions, can be well represented by systems of Partial Differential Equations. In this paper, a numerical procedure is proposed for the fast and robust solution of flow and transport problems in 2D heterogeneous saturated media. The governing equations are spatially discretized with unstructured triangular meshes that must satisfy the Delaunay condition. The solution of the flow problem is split from the solution of the transport problem and it is obtained with an approach similar to the Mixed Hybrid Finite Elements method, that always guarantees the M-property of the resulting linear system. The transport problem is solved applying a prediction/correction procedure. The prediction step analytically solves the convective/reactive components in the context of a MAST Finite Volume scheme. The correction step computes the anisotropic diffusive components in the context of a recently proposed Finite Elements scheme. Massa balance is locally and globally satisfied in all the solution steps. Convergence order and computational costs are investigated and model results are compared with literature ones.

Local mass conservative Hermite interpolation for the solution of flow problems by a multi-domain boundary element approach

This paper presents a local Hermite radial basis function interpolation scheme for the velocity and pressure fields. The interpolation for velocity satisfies the continuity equation (mass conservative interpolation) while the pressure interpolation obeys the pressure equation. Additionally, the Dual Reciprocity Boundary Element method (DRBEM) is applied to obtain an integral representation of the Navier–Stokes equations. Then, the proposed local interpolation is used to obtain the values of the field variables and their partial derivatives at the boundary of the sub-domains. This interpolation allows one to obtain the boundary values needed for the integral formulas for velocity and pressure at some nodes within the sub-domains. In the proposed approach the boundary elements are merely used to parameterize the geometry, but not for the evaluation of the integrals as it is usually done. The presented multi-domain approach is different from the traditional ones in boundary elements because the resulting integral equations are non singular and the boundary data needed for the boundary integrals are approximated using a local interpolation. Some accurate results for simple Stokes problems and for the Navier–Stokes equations at low Reynolds numbers up to Re = 400 were obtained.