Flux-corrected Transport Research Articles

A 2D Meshless Solver Based on AUSM+ and MUSCL Scheme

When solving Euler equations of fluid dynamics around complex configurations, a meshless method which doesn’t use the information of the meshes may have the advantages to simulate the flow field. In this paper, a simple and accurate meshless algorithm based on AUSM+ and MUSCL scheme has been described. To assess the capability for capturing shock position and the resolvability of the complex shock waves, a number of typical test cases are calculated with the meshless method. The results obtained are in good agreement with the exact solution or some high-resolution numerical method as well as flux-corrected transport (FCT) algorithm with adaptive mesh refinement (AMR) technique.

A geometrically-conservative, synchronized, flux-corrected remap for arbitrary Lagrangian–Eulerian computations with nodal finite elements

This article describes a conservative synchronized remap algorithm applicable to arbitrary Lagrangian–Eulerian computations with nodal finite elements. In the proposed approach, ideas derived from flux-corrected transport (FCT) methods are extended to conservative remap. Unique to the proposed method is the direct incorporation of the geometric conservation law (GCL) in the resulting numerical scheme. It is shown here that the geometric conservation law allows the method to inherit the positivity preserving and local extrema diminishing (LED) properties typical of FCT schemes. The proposed framework is extended to the systems of equations that typically arise in meteorological and compressible flow computations. The proposed algorithm remaps the vector fields associated with these problems by means of a synchronized strategy. The present paper also complements and extends the work of the second author on nodal-based methods for shock hydrodynamics, delivering a fully integrated suite of Lagrangian/remap algorithms for computations of compressible materials under extreme load conditions. Extensive testing in one, two, and three dimensions shows that the method is robust and accurate under typical computational scenarios.

A positivity-preserving ALE finite element scheme for convection–diffusion equations in moving domains

A new high-resolution scheme is developed for convection–diffusion problems in domains with moving boundaries. A finite element approximation of the governing equation is designed within the framework of a conservative Arbitrary Lagrangian Eulerian (ALE) formulation. An implicit flux-corrected transport (FCT) algorithm is implemented to suppress spurious undershoots and overshoots appearing in convection-dominated problems. A detailed numerical study is performed for P 1 finite element discretizations on fixed and moving meshes. Simulation results for a Taylor dispersion problem (moderate Peclet numbers) and for a convection-dominated problem (large Peclet numbers) are presented to give a flavor of practical applications.

Simulation of current layer dynamics in the magnetogasdynamic interaction with an argon flow

A nonstationary three-dimensional magnetohydrodynamic (MHD) model is used to numerically simulate the formation of a current layer interacting with a transverse magnetic field in a supersonic argon flow. The structural features of the current layer and the characteristics of the process are analyzed at various intensities of the MHD interaction. The problem is solved using the MacCormack method with splitting in spatial coordinates and flux-corrected transport.

Optimal Design of a Grid-Cathode Structure in a Spherically Convergent Beam Fusion Device by Response-Surface Methodology Combined With Experimental Design

To apply fusion energy through a spherically convergent beam fusion (SCBF) device as a portable neutron source, neutron production is very important. The rate of production is greatly dependent upon the ion current, which is closely related to the potential-well structure within a grid cathode. In this paper, we propose a design method by varying the cathode-ring sizes to produce an optimal grid-cathode structure in an SCBF device. The optimization is based on response-surface methodology (RSM); however, full factorial design is also applied to increase the precision of optimization and reduce experiment iteration in the application of RSM. The finite-element method, combined with the flux-corrected transport algorithm, is employed to calculate the ion current. From the optimized model, a higher ion current is calculated, resulting in a deeper potential well.

A multistep flux-corrected transport scheme

A multistep flux-corrected transport (MFCT) scheme is developed to achieve conservative and monotonic tracer transports for multistep dynamical cores. MFCT extends Zalesak two-time level scheme to any multistep time-differencing schemes by including multiple high-order fluxes in the antidiffusive flux, while computing the two-time level low-order monotone solution. The multistep time-differencing scheme used in this study is the third-order Adams–Bashforth (AB3) scheme implemented in a finite-volume icosahedral shallow-water model. The accuracy of AB3 MFCT is quantified by the shape-preserving advection experiments in non-divergent flow, as well as a cosine bell whose shape changes during advection in shear flow. AB3 MFCT has been shown to be insensitive to time step size. This make AB3 MFCT an attractive transport scheme for explicit high resolution model applications with small time step. MFCT is tested in shallow-water model simulations to demonstrate that the use of MFCT maintains positive-definite tracer transport, while at the same time conserving both fluid mass and tracer mass within round-off errors in the AB3 dynamic core.

FEM–FCT-Based Dynamic Simulation of Corona Discharge in Point–Plane Configuration

In this paper, a numerical algorithm for the simulation of the dynamic corona discharge in air is proposed assuming single-species charge carriers. The simulation results show the behavior of corona current and space-charge density under two waveforms of the applied voltage: step and pulse. The electric field is calculated by means of the finite-element method, and the flux-corrected transport technique is utilized for the space-charge-density calculations.

Failsafe flux limiting and constrained data projections for equations of gas dynamics

A new approach to flux limiting for systems of conservation laws is presented. The Galerkin finite element discretization/ L 2 projection is equipped with a failsafe mechanism that prevents the birth and growth of spurious local extrema. Within the framework of a synchronized flux-corrected transport (FCT) algorithm, the velocity and pressure fields are constrained using node-by-node transformations from the conservative to the primitive variables. An additional correction step is included to ensure that all the quantities of interest (density, velocity, pressure) are bounded by the physically admissible low-order values. The result is a conservative and bounded scheme with low numerical diffusion. The new failsafe FCT limiter is integrated into a high-resolution finite element scheme for the Euler equations of gas dynamics. Also, bounded L 2 projection operators for conservative interpolation/initialization are designed. The performance of the proposed limiting strategy and the need for a posteriori control of flux-corrected solutions are illustrated by numerical examples.

The effects of acoustic streaming on thermal convection in an enclosure with differentially heated horizontal walls

The effects of classical and irregular streaming motion on convective heat transfer in air-filled shallow enclosures carrying a standing sound wave are investigated. The fluid motion is driven by the periodic vibration of the enclosure left wall. The vertical walls of the enclosure are adiabatic while the horizontal walls are heated differentially. The fully compressible form of the Navier–Stokes equations are considered to compute the oscillatory and mean flow fields. A control-volume method based, explicit time-marching Flux-Corrected Transport (FCT) Algorithm is used to simulate the transport phenomena in the enclosure. The simulation results of a test case for an unheated enclosure are compared with the existing literature for code validation. Transverse temperature gradient strongly affects the acoustic streaming structures and velocities. The streaming motion significantly enhances overall heat transfer from the bottom wall compared to pure conduction. Enhancement is more pronounced in the presence of irregular streaming.

3-D numerical analysis of EHD turbulent flow and mono-disperse charged particle transport and collection in a wire-plate ESP

The present study attempts to develop a detailed numerical approach and a simulation procedure to predict the motion of gas, ions and particles inside a simple parallel plate channel containing a single corona wire. A hybrid Finite Element (FEM)-Flux Corrected Transport (FCT)-Finite Volume (FVM) method is used: the FEM–FCT numerical algorithm is applied for modeling the steady-state corona discharge, while the turbulent gas flow and the particle motion under electrostatic forces are modeled using the commercial CFD code FLUENT. Calculations for the gas flow are carried out by solving the Reynolds-averaged Navier–Stokes equations and turbulence is modeled using the k– ɛ turbulence model. An additional source term is added to the gas flow equation to include the effect of the electric field, obtained by solving a coupled system of the electric field and charge transport equations using User-Defined Functions (UDFs). The particle phase is simulated based on the Lagrangian approach, where a large number of particles is traced with their motion affected by the gas flow and electrostatic forces using the Discrete Phase Model (DPM) in FLUENT. The developed model is useful to gain insight into the particle collection phenomena that take place inside an ESP.

Highly Accurate Schemes for PDE-Based Morphology with General Convex Structuring Elements

The two fundamental operations in morphological image processing are dilation and erosion. These processes are defined via structuring elements. It is of practical interest to consider a variety of structuring element shapes. The realisation of dilation/erosion for convex structuring elements by use of partial differential equations (PDEs) allows for digital scalability and subpixel accuracy. However, numerical schemes suffer from blur by dissipative artifacts. In our paper we present a family of so-called flux-corrected transport (FCT) schemes that addresses this problem for arbitrary convex structuring elements. The main characteristics of the FCT-schemes are: (i) They keep edges very sharp during the morphological evolution process, and (ii) they feature a high degree of rotational invariance. We validate the FCT-scheme theoretically by proving consistency and stability. Numerical experiments with diamonds and ellipses as structuring elements show that FCT-schemes are superior to standard schemes in the field of PDE-based morphology.

Nonzero Mean Oscillatory Flow in Symmetrically-Heated Shallow Enclosures: An Analysis of Acoustic Streaming

The effects of symmetric heating on a nonzero mean oscillatory fluid motion, namely acoustic streaming, in air-filled shallow enclosures and associated thermal convection in transient regime are investigated numerically. The fluid motion is driven by periodic vibration of the enclosure left wall. The vertical walls of the enclosure are adiabatic while the horizontal walls are heated symmetrically. A control-volume method-based explicit time-marching flux-corrected transport algorithm is used to simulate the transport phenomena in the enclosure. A symmetric temperature gradient strongly affects the acoustic streaming structures and velocities. The variation of the steady flow field becomes more noticeable and drastic with increasing wall temperature.

A numerical investigation of the effects of a transverse temperature gradient on the formation of regular and irregular acoustic streaming in an enclosure

The effects of a transverse temperature gradient on the formation of regular and irregular acoustic streaming structures in air-filled, two-dimensional, rectangular, shallow enclosures carrying a longitudinal sound field are investigated numerically. The fluid motion is induced by the harmonic vibration of the enclosure left wall. The fully compressible form of the Navier—Stokes equations is considered to predict the primary oscillatory and secondary pseudo-steady streaming flow fields. An explicit time-marching flux-corrected transport algorithm is used to simulate the acoustic wave formation, propagation, and the resulting flow patterns in the enclosure. The vertical walls of the enclosure are adiabatic whereas the horizontal walls are heated differentially or symmetrically. The transverse temperature gradients are found to strongly affect the acoustic streaming structures and the velocities. The steady streaming velocities significantly increase when the enclosure horizontal walls are asymmetrically heated for both regular and irregular streaming flows. For irregular streaming, the transverse temperature gradients completely change the flow patterns. The irregular streaming velocities are greatly reduced in case of the symmetric temperature increase of the horizontal walls.

Numerical Modelling of Nitrogen Thermal Effects Produced by the Negative DC Corona Discharge

In this work, we simulate numerically the thermal effects in nitrogen at atmospheric pressure caused by a negative corona DC discharge of low current. A mathematical function that simulates the injection of the thermal transfer in gas is proposed. The simulated discharge is of a negative point to plane mass type, with an interelectrode distance of 12 mm and a symmetry about the axis of discharge. The spatial and temporal evolution of neutrals is analyzed based upon the equations of continuity, momentum and energy in a cylindrical geometry. For the geometry of the system, the FCT (flux corrected transport) procedure was adopted.

An unsplit lagrangian advection scheme for volume of fluid method

An Unsplit Lagrangian Advection (ULA) scheme for Volume Of Fluid (VOF) method is presented in this article. The ULA scheme is developed based on an algorithm of Piecewise Linear Interface Construction (PLIC). The volume fluxes between cells are calculated through solving the new equation of the linear interfaces in cells in the ULA scheme. The fluxes flowing out from one cell is the inflow fluxes for another cell. In this way the whole fluid volume is conserved strictly without using any redistribution algorithms. The ULA scheme is based on two-dimensional structured rectangular mesh and may be extended to three-dimensional structured mesh with more geometrical efforts. The results from three widely-used benchmark tests show that the ULA scheme can achieve the accuracy higher than Split Lagaragian Advection (SLA) scheme and the Flux-Corrected Transport (FCT) algorithm.

Numerical simulation of reactive flow in liquid composite molding using flux-corrected transport (FCT) based finite element/control volume (FE/CV) method

The mold-filling simulation of liquid composite molding (LCM) is of great importance in optimizing this cost-effective polymer-composites manufacturing process. The flow in LCM is a convection-dominated reactive, non-isothermal flow involving a moving boundary, so the Galerkin finite element method (FEM) has to be adapted with stabilization techniques to solve such problems. The streamline-upwind Petrov–Galerkin (SUPG) method is one of the most popular stabilized methods. However, the use of SUPG still leads to localized numerical wiggles in the vicinity of sharp solution gradients, which is often encountered in the 3D mold-filling simulation of LCM for thick parts. In this study, we propose to use the flux-corrected transport (FCT) based FEM to solve a set of highly convective transport equations. The numerical examples presented in this paper demonstrate the excellent performance of FCT based FEM in suppressing spurious oscillations in the regions of steep solution-gradients as opposed to the numerical instability of SUPG in such regions. For the first time, the FCT based FEM combined with the control-volume method is employed to simulate the non-isothermal mold-filling process in LCM. We have developed a simulation code PORE-FLOW© based on the scheme proposed in the study. Numerical studies have proven the stability of the FCT based FEM while modeling the mold-filling process of LCM.

Adaptive non-convex total variation regularisation for image restoration

An adaptive non-convex total variation regularisation is proposed for blind image restoration. A flux corrected transport (FCT) technique is used to obtain a stable numerical scheme, where a spatially varying constraint allows a better restoration of image edges and fine detail. Finally, its advantages are shown in deblurring edges, denoising and restoring fine details of image simultaneously in experiments.

Transient Shock Formation of Pulsed Electrothermal Plasma Discharge Confined in an Extended Bore

An electrothermal gun possesses a great potential to be an efficient source of pulsed plasma discharge for nanomaterials production or thermal plasma spray coatings. A plasma discharge by intense pulsed power is numerically studied utilizing time-dependent gas dynamics equations which are solved by FCT (flux-corrected transport) algorithm in two-dimensional domain of the interior capillary bore region and the external region of extended bore. Plasma conditions at the bore exit, mass ablation of polycarbonate bore wall, and degree of ionization are determined at different levels of transient arc current profile. As a way to controlling the plasma discharge, the extended bore at the capillary exit is considered and the flow pattern of pulsed plasma discharge in the extended bore exhibit complex shock structure from slightly to highly underexpanded jet depending on the level of arc current profiles. Flow instability of oscillating Mach disk is found at higher level of arc current profile cases.

Development of a sub-scale dynamics model for pressure relaxation of multi-material cells in Lagrangian hydrodynamics

We have extended the Sub-Scale Dynamics (SSD) closure model for multi-fluid computational cells. Volume exchange between two materials is based on the interface area and a notional interface translation velocity, which is derived from a linearized Riemann solution. We have extended the model to cells with any number of materials, computing pressure-difference-driven volume and energy exchange as the algebraic sum of pairwise interactions. In multiple dimensions, we rely on interface reconstruction to provide interface areas and orientations, and centroids of material polygons. In order to prevent unphysically large or unmanageably small material volumes, we have used a flux-corrected transport (FCT) approach to limit the pressure-driven part of the volume exchange. We describe the implementation of this model in two dimensions in the FLAG hydrodynamics code. We also report on Lagrangian test calculations, comparing them with others made using a mixed-zone closure model due to Tipton, and with corresponding calculations made with only single-material cells. We find that in some cases, the SSD model more accurately predicts the state of material in mixed cells. By comparing the algebraic forms of both models, we identify similar dependencies on state and dynamical variables, and propose explanations for the apparent higher fidelity of the SSD model.

A Flux-Corrected Finite Element Method for Chemotaxis Problems

AbstractAn implicit flux-corrected transport (FCT) algorithm has been developed for a class of chemotaxis models. The coefficients of the Galerkin finite element discretization has been adjusted in such a way as to guarantee mass conservation and keep the cell density nonnegative. The numerical behaviour of the proposed highresolution scheme is tested on the blow-up problem for a minimal chemotaxis model with singularities. It has also been shown that the results for an Escherichia coli chemotaxis model are in good agreement with the experimental data reported in the literature.