Navier-Stokes Model Research Articles

CFD assessment of RANS turbulence modeling for solidification in internal flows against experiments and higher fidelity LBM-LES phase change model

Generation-IV nuclear reactors’ potential coolant candidates include molten salts and liquid metals. Owing to their high melting temperature, both the design and safety assessments of these reactors need to take into consideration potential solidification events during normal or abnormal operation. This work assesses the Finite Volume Computational Fluid Dynamics (FV-CFD) enthalpy-porosity method combined with the Reynolds Averaged Navier Stokes (RANS) model k−ω to model internal solidification under turbulent flow conditions for high and low Prandtl numbers at a moderate computational cost, which is required for full-core nuclear reactor analyses. Concerning high Prandtl numbers, the predictions of macroscopic quantities generated by the FV-CFD RANS model are contrasted against a well-known internal solidification experiment on water (Thomason et al., 1978). A key factor in the satisfactory agreement between the CFD RANS model and the experiment is the addition of an interface turbulence-damping source to the specific dissipation rate equation (ω). For the low Prandtl numbers involved in liquid metals, there is a lack of high-fidelity experiments due to the complicated measurements. Thus, to perform the FV-CFD RANS model assessment, we develop and validate a high-fidelity phase-change model based on the Lattice Boltzmann Method (LBM) with a Large Eddy Simulation (LES) turbulence model. To the author’s knowledge, this is the first attempt to integrate LES turbulence models with phase-change solidification in the LBM context. Considering the computational time advantage of the FV-CFD RANS model over higher fidelity models and the good agreement of its predictions against experiments and the LES model demonstrated, this work demonstrates that FV-CFD RANS is an attractive tool to model internal turbulent solidification.

Constrained Recalibration of Reynolds-Averaged Navier–Stokes Models

The constants and functions in Reynolds-averaged Navier–Stokes (RANS) turbulence models are coupled. Consequently, modifications of a RANS model often negatively impact its basic calibrations, which is why machine-learned augmentations are often detrimental outside the training dataset. A solution to this is to identify the degrees of freedom that do not affect the basic calibrations and only modify these identified degrees of freedom when recalibrating the baseline model to accommodate a specific application. This approach is colloquially known as the “rubber-band” approach, which we formally call “constrained model recalibration” in this paper. To illustrate the efficacy of the approach, we identify the degrees of freedom in the Spalart–Allmaras model that do not affect the log law calibration. By subsequently interfacing data-based methods with these degrees of freedom, we train models to solve historically challenging flow scenarios, including the round-jet/plane-jet anomaly, airfoil stall, secondary flow separation, and recovery after separation. In addition to good performance inside the training dataset, the trained models yield similar performance as the baseline model outside the training dataset.

How far do indirect signal production mechanisms influence regularity in the three-dimensional Keller–Segel–Navier–Stokes system?

This paper reconsiders the Keller–Segel–Navier–Stokes model with indirect signal production and weak logistic-type degradation in a three-dimensional (3D) bounded and smooth domain. One recent literature has asserted that for all reasonably regular initial data, the associated initial-boundary value problem with certain sub-quadratic degradation possesses at least one global generalized solution which is uniformly bounded and converges to the constant equilibrium in [Formula: see text] with any [Formula: see text]. Nevertheless, the knowledge on regularity properties of solution has not yet exceeded some information on fairly basic integrability features. The present study firstly elevates the regularities of some solution components under the same assumption on degradation exponent, especially establishes the global boundedness in [Formula: see text] with [Formula: see text], and secondly asserts that each of these generalized solutions becomes eventually classical and bounded in [Formula: see text] under some suitably strong sub-quadratic degradation assumption and an explicit smallness condition on the intrinsic growth rate of cells relative to some powers of the degradation coefficient. As a by-product of the latter, these solutions are shown to stabilize toward the corresponding spatially homogeneous state in [Formula: see text]. Our results indeed provide a more in-depth understanding on the global dynamics of solutions, and significantly improve previously known ones. In comparison to the related contributions in the case of direct signal production, our findings inter alia rigorously reveal that the indirect signal production mechanism results in some genuine regularizing effects in the sense that the possibly destabilizing action of chemotactic cross-diffusion in the 3D Keller–Segel–Navier–Stokes system can be greatly weakened or even completely excluded by this indirectness.

Computational Fluid Dynamics: Flow Analysis on The Effect of Different Jet Orifice Angle Multi Circular Jet for Fuel and Air Mixing

The mixing of fuel and air plays a major role in the spray and flame behavior, hence affecting the combustion performance and emissions of the internal mixing air-assisted atomizers. Air-assisted atomizers are introduced to counter the low-pressure differential of a simplex nozzle, which reduces the atomization quality. The present study aims to determine the effects of Multi Circular Jet (MCJ) plates on the geometrical configurations of internal flows in mixing chamber and the internal flow of plate 3 using different properties of fuel. In this study, the realizable k-ε turbulence model, specifically designed for strongly swirling flows, is validated through numerical simulations. The turbulence model selected is a type of Reynolds averaged Navier-Stokes (RANS) model called the k-ε model. The MCJ plates provide the primary air entrance into the mixing chamber. Additionally, it acts as a turbulence generator and can be adjusted to alter the flow of fuel and air mixtures in a mixing chamber. The study compares several MCJ geometries in terms of pressure, speed, turbulent kinetic energy, and volume fraction and compares the performances of diesel and Crude Palm Oil (CPO) B30 biodiesel fuels. The findings imply that CPO B30 biodiesel has superior atomization and mixing due to its higher density and turbulent kinetic energy. CPO B30 biodiesel was compared to Diesel in terms of maximum pressure, average speed, turbulent kinetic energy per unit mass, and volume fraction. The results indicate that CPO B30 has lower pressure and higher velocity than Diesel, suggesting better fuel atomization and mixing. The higher density of CPO B30 leads to increased turbulent kinetic energy, improving fuel-air mixing inside the combustion chamber. The study demonstrates that the use of MCJ plates can enhance mixing in a mixing chamber. In addition, MCJ plates show the ability to control the spray and atomization. The findings of this study contribute to a better understanding of the relationships between geometry and fuel-air mixing, as well as the characteristics of the internal mixing air-assisted atomizer, which will lead to future burner system improvements.

Discontinuous Galerkin Two-Grid Method for the Transient Navier–Stokes Equations

Abstract In this paper, we apply a two-grid scheme to the DG formulation of the 2D transient Navier–Stokes model. The two-grid algorithm consists of the following steps: Step 1 involves solving the nonlinear system on a coarse mesh with mesh size 𝐻, and Step 2 involves linearizing the nonlinear system by using the coarse grid solution on a fine mesh of mesh size ℎ and solving the resulting system to produce an approximate solution with desired accuracy. We establish optimal error estimates of the two-grid DG approximations for the velocity and pressure in energy and L 2 L^{2} -norms, respectively, for an appropriate choice of coarse and fine mesh parameters. We further discretize the two-grid DG model in time, using the backward Euler method, and derive the fully discrete error estimates. Finally, numerical results are presented to confirm the efficiency of the proposed scheme.

Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity.

Two Reynolds-averaged Navier-Stokes models with full Reynolds-stress transport (RST) and tensor eddy viscosity are presented. These new models represent RST extensions of the k-2L-a-C and k-ϕ-L-a-C models by Morgan [Phys. Rev. E 103, 053108 (2021)10.1103/PhysRevE.103.053108; Phys. Rev. E 105, 045104 (2022)10.1103/PhysRevE.105.045104]. Self-similarity analysis is used to derive constraints on model coefficients required to reproduce expected growth parameters for a variety of canonical flows, including Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) mixing layers. Both models are then applied in one-dimensional simulation of RT and KH mixing layers, and the expected self-similar growth rates and anisotropy are obtained. Next, models are applied in two-dimensional simulation of the so-called "tilted rocket rig" inclined RT experiment [J. Fluids Eng. 136, 091212 (2014)10.1115/1.4027587] and in simulation of a shock-accelerated localized patch of turbulence. It is found that RST is required to capture the qualitative growth of the shock-accelerated patch, and an anisotropic eddy viscosity provides substantial improvement over a Boussinesq treatment for the tilted rocket rig problem.

Dynamic simulation and analysis of the influence of urethral morphological changes on urodynamics after benign prostatic hyperplasia surgery: A computational fluid dynamics study

Background and objectiveComputational fluid dynamics (CFD) technology has been widely used in medicine to simulate and analyse urine flow characteristics in urology. In previous studies, researchers have modelled the analysis with a simple circular urethra, ignoring the effect of the patient's true urethral morphology on the urinary flow rate. Moreover, the studies tended to be steady-state simulations rather than dynamic simulations. Therefore, this study is established a relatively realistic model of the posterior urethra based on MRI data combined with the urodynamic data of patients and analysed the urodynamic characteristics of the posterior urethra model after benign prostatic hyperplasia (BPH) surgery using a CFD dynamic simulation. MethodsBased on clinical MRI data, a three-dimensional real urethral model was established for two patients with BPH after surgery. The boundary conditions were set according to the patients’ real urodynamic data, and a Reynolds averaged Navier‒Stokes model was used for transient simulations. The dynamic simulation depicted the entire urination process, and the urine flow characteristics were studied under real urethral morphology after surgery. Results1. By comparing the three-dimensional trajectory of urine and the vortex identification cloud map based on the Q criterion, we intuitively observed the distribution of the vortex in the model, and a ‘gourd-shaped’ urethra was more likely to generate a vortex than a ‘funnel-shaped’ urethra. 2. After surgery for BPH, the changes in the posterior urethral pressure were mainly concentrated in the urethral membrane, and the velocity increased while the pressure decreased. The curve of the posterior urethral pressure changes during urination was simulated and calculated. The posterior urethral pressure gradients of the two patients were 6.6 cmH2O and 5.26 cmH2O. ConclusionsThe complete urinary discharge process can be dynamically simulated using CFD techniques. By comparing the simulation results, the posterior urethral morphology can have an important impact on the urinary flow characteristics. Determining the location of vortex generation can lay a foundation for personalized surgical plans for patients in the future. Furthermore, numerical simulations can provide a new method for the study of non-invasive posterior urethral pressure gradients.

Numerical simulations of granular dam break: Comparison between discrete element, Navier-Stokes, and thin-layer models.

Granular flows occur in various contexts, including laboratory experiments, industrial processes, and natural geophysical flows. To investigate their dynamics, different kinds of physically based models have been developed. These models can be characterized by the length scale at which dynamic processes are described. Discrete models use a microscopic scale to individually model each grain, Navier-Stokes models use a mesoscopic scale to consider elementary volumes of grains, and thin-layer models use a macroscopic scale to model the dynamics of elementary columns of fluids. In each case, the derivation of the associated equationsis well-known. However, few studies focus on the extent to which these modeling solutions yield mutually coherent results. In this article, we compare the simulations of a granular dam break on a horizontal or inclined planes for the discrete model convex optimization contact dynamics (COCD), the Navier-Stokes model Basilisk, and the thin-layer depth-averaged model SHALTOP. We show that, although all three models allow reproducing the temporal evolution of the free surface in the horizontal case (except for SHALTOP at the initiation), the modeled flow dynamics are significantly different, and, in particular, during the stopping phase. The stresses measured at the flow's bottom, reflecting the flow dynamics, are in relatively good agreement, but significant variations are obtained with the COCD model due to complex and fast-varying granular lattices. Similar conclusions are drawn using the same rheological parameters to model a granular dam break on an inclined plane. This comparison exercise is essential for assessing the limits and uncertainties of granular flow modeling.

Unsteady Reynolds-Averaged Navier–Stokes Simulations of a Ducted Wind Turbine

Abstract An unsteady Reynolds-averaged Navier–Stokes model on body-fitted meshes in a commercial package (SimericsMP+) with a mismatched grid interface is used to study fluid dynamics around a ducted wind turbine. The model is validated by studying turbulent flow past a marine propeller. The nondimensional thrust and torque coefficients are compared against experimental data and results from a large eddy simulation model. Both coefficients are found to be within 3% of experimental results. Following this validation, the impact of different tip speed ratios on the ducted wind turbine's fluid dynamics is assessed. The optimal tip speed ratio is found to be the design value of 3.93 with a maximum power coefficient of 0.465 based on the duct exit area. The corresponding thrust coefficient is found to be 1.02 based on the rotor area. Lower tip speed ratios experience larger flow separation on the duct interior. Higher tip speed ratios decrease the size of the low-velocity region behind the hub. The ducted wind turbine's performance at design conditions is compared to an open rotor. The ducted wind turbine increases the power coefficient by 96% over the open rotor. The impact of hub size on the ducted wind turbine is also studied by simulating a smaller hub with 77% diameter. At the design tip speed ratio, the smaller hub has a power coefficient of 0.417. The maximum power coefficient is found to be 0.446 at a higher tip speed ratio of 4.5.

Identifying bioclimatic techniques for sustainable low-rise high-density residential units: Comparative analysis on the ventilation performance of vernacular dwellings in China

Vernacular dwellings equipped with bioclimatic techniques, used to form low-rise high-density communities in most Asian regions, are of great value for the development of modern sustainable residential units. Natural ventilation is a major concern mainly because of its climate-related characteristics of improving indoor thermal comfort at extremely low ecological costs. Therefore, this study applies a comparative analysis coupled with field investigations and numerical simulations to the ventilation technologies of vernacular dwellings in different areas of China. Geometric prototypes of typical vernacular dwellings in six climate zones were generated based on field measurements. Computational Fluid Dynamic (CFD) simulations were conducted in OpenFOAM with the Reynolds Averaged Navier-Stokes (RANS) modeling approach and the RNG k-ε turbulence model. A correlation analysis of the building elements and climate factors was also performed to determine the relevant parameters affecting ventilation performance. The results revealed different emphases and verified strategies for wind environment regulation based on different local climates. Six physical parameters, namely wind projection angle, orientation, wind inclination angle, window-to-wall ratio, top-to-bottom ratio, and height-to-width ratio of the atrium, are considered to be closely related to ventilation efficiency. The findings from the current research provide quantitative evidence of the effectiveness of natural ventilation technologies of vernacular dwellings and contribute to comprehensive knowledge for designing sustainable low-rise high-density residential units with optimum ventilation functions.

Flow enhancement from wall pressure observations: A compressible continuous adjoint data assimilation model

This study establishes a compressible continuous adjoint data assimilation (C2ADA) approach for reproducing a complete mean flow from sparse wall pressure observations. The model-form error induced by the Boussinesq approximation is corrected by the addition of a spatially varying additive forcing term. The linear part of the eddy viscosity, computed using the conventional Reynolds-averaged Navier–Stokes model, is incorporated for ensuring the well-posedness of the optimization. The model is derived theoretically to minimize discrepancies between the wall pressure measurements and the numerical predictions of the primary-adjoint system, thereby enabling determination of the optimal contribution of the Reynolds force vector. The effects of divergence schemes and turbulence models are investigated by examining flow over a 30P30N airfoil. The C2ADA model, employing two distinct schemes, demonstrates significant improvements in velocity estimation, but the first-order scheme introduces excessive dissipation, resulting in an under-prediction of spanwise vorticity. The C2ADA model combined with different eddy-viscosity models uniquely recovers the Reynolds force vectors and obtains mean fields that outperform those achieved solely through conventional eddy viscosity models. The practicability of the C2ADA model for capturing complex flow phenomena is confirmed by applying it to study three-dimensional flow over a 65° delta wing. Despite limited wall pressure observations, the C2ADA model has shown a notable improvement in accurately estimating the intensity and location of both the primary and secondary vortices. Recovery errors in the apex region are significantly diminished by incorporating a paucity of observations account for the effect of inboard vortex. The study broadens the applicability of continuous adjoint-based approaches for modeling compressible flow, as our C2ADA approach is easily implemented in existing computational fluid dynamics solvers and has significantly higher computational efficiency than other approaches.

Effect models for the stationary Navier–Stokes fluid in a porous medium with different scales

In this paper, we investigate an incompressible flow through a thin corrugated domain fill with fluid saturated porous medium. The porous medium flow is governed by Navier–Stokes model. The thickness of the domain is assumed to be aɛ and the solid part is supposed to be periodical cylinders of size ɛ. We rigorously derive different asymptotic models by comparing the relation between ɛ and aɛ. To prove the main results, we employ the homogenization technique based on the generalized Poincaré inequality.

Testing a Generalized Two-Equation Turbulence Model for Computational Aerodynamics of a Mid-Range Aircraft

The generalized k-ω formulation provides a relatively new flexible eddy-viscosity Reynolds-averaged Navier–Stokes modeling approach to turbulent flow simulation, where free coefficients allow for fine-tuning and optimal adjusting of the turbulence closure procedure. The present study addressed the calibration of this versatile model for the aerodynamic design of an innovative mid-range commercial airplane by carrying out a series of simulations for varying model coefficients. Comparing the different solutions with each other, as well as with reference experimental and higher-fidelity numerical data, the performance of the generalized procedure in predicting the aerodynamic loading on the aircraft model was systematically examined. While drawing particular attention to the high-lift regime, the set of model parameters giving the best results was practically determined.

Prediction of urban airflow fields around isolated high-rise buildings using data-driven non-linear correction models

When it comes to predicting urban airflow, steady Reynolds-averaged Navier-Stokes (SRANS) models that rely on Reynolds stress often face a challenge called the closure problem. This problem involves unresolved structural flaws and uncertainties in the closure coefficients used in the models. Previous attempts to recalibrate coefficients for specific urban flows without breaking the linear constitutive relation have resulted in simulation results constrained by the baseline turbulence model. Therefore, this study aims to enhance the performance of SRANS models by addressing these structural flaws. To achieve this, a novel data-driven framework is proposed. It leverages the deterministic symbolic regression algorithm to discover explicit algebraic expressions for a non-linear Reynolds stress correction model. The robustness of the correction model is ensured by maintaining the linear eddy viscosity model for iterative calculations while keeping the non-linear component frozen. The proposed framework is evaluated using three isolated building cases with varying geometric configurations and inflow boundary conditions. Findings demonstrate that computational fluid dynamics (CFD) predictions incorporating the data-driven non-linear correction model consistently align closer to wind tunnel experimental results compared to both standard and non-linear versions of the k-ε turbulence model. This improvement is reflected in reduced reattachment lengths and more accurate mean velocity distributions in the wake of buildings. However, it should be noted that there is a possibility of overpredicting wind velocity in the windward area. This study introduces valuable insights and additional strategies to enhance the prediction accuracy of SRANS models in urban airflow simulations.

Local turbulence generation using conditional generative adversarial networks toward Reynolds-averaged Navier–Stokes modeling

Data-driven turbulence modeling has been extensively studied in recent years. To date, only high-fidelity data from the mean flow field have been used for Reynolds-averaged Navier–Stokes (RANS) modeling, while the instantaneous turbulence fields from direct numerical simulation and large eddy simulation simulations have not been utilized. In this paper, a new framework is proposed to augment machine learning RANS modeling with features extracted from instantaneous turbulence flow data. A conditional generative model is trained to model the probability distribution of the local instantaneous turbulence field given local mean flow features. Then, the generative model is transferred to machine learning RANS modeling. The present work is mainly focused on generating a local instantaneous turbulence field using conditional generative adversarial networks (CGANs). Several GANs are trained first on the turbulence data from channel flow and periodic hill flow to generate complete one-dimensional and two-dimensional turbulence fields. Then, a CGAN is trained on the periodic hill flow data to generate local turbulence fields. Statistical analysis is performed on the generated samples from the GAN models. The first and second moments, the two-point correlation, and the energy spectra conform well to those of real turbulence. Finally, the information learned by the CGAN is used for machine learning RANS modeling by multitask learning, and the feasibility of the framework proposed in this paper is initially verified.

Best modeling practice for self-propulsion simulation of ship model in calm water

This paper presents the development of best Reynolds-Averaged Navier–Stokes modeling practices for simulations of propeller–hull interaction in calm water using Star-CCM+. Extensive convergence studies were carried out to examine effects of various propeller modeling methods and parameters, such as non-dimensional wall distance, grid resolution/distribution, and turbulence model. Bare-hull resistance and propeller open-water performance were first examined. For propeller–hull interaction, a simplified body-force method and a detailed propeller modeling method were applied to predict the wake fraction and propeller performance behind the hull. The difference in accuracy of the two methods was quantified, and the best modeling practices were recommended based on the convergence studies. Validation studies were carried out for the Korea Research Institute of Ships and Ocean Engineering Container Ship model. The pseudo-effective wake fraction determined from computational fluid dynamics simulations was introduced and compared with the experimental effective wake fraction.

Deep-learning-based reduced-order modeling to optimize recuperative burner operating conditions

This study analyzed a recuperative burner system that is critical for energy efficiency and pollutant reduction in the firing processes required in the manufacturing industries. We aimed to optimize the operating conditions of a recuperative burner using computational fluid dynamics (CFD) combined with a novel reduced-order deep-learning technique. The Reynolds-averaged Navier–Stokes model and finite-rate/eddy-dissipation models were used to generate reliable CFD simulation results considering four operating conditions (temperature and mass flow rate of air and fuel). We first validated the CFD model with two-dimensional axis-symmetric experimental burner results and created a proper orthogonal decomposition transformer model using large-scale snapshots of the CFD results and various operating conditions. Subsequently, a genetic algorithm was employed to find the optimal conditions for five different objective functions: fuel economy, decrease in carbon monoxide emissions, reduction in nitrogen oxide emissions, decrease in carbon dioxide production, and an all-encompassing view of the four objectives. Finally, by comparing our proposed approach with previous methods, we confirmed that the obtained optimal operating conditions improve the performance of the recuperative burner. This study provides an optimized framework for recuperative burners to reduce environmental pollution, with potential applications in many industries, such as ceramics, steel, and batteries.

Assessment of Computational Fluid Dynamics Reynolds-Averaged Navier–Stokes Models for Bluff Bodies Aerodynamics

<div>Since the steady-state computational fluid dynamics (CFD) Reynolds-averaged Navier–Stokes (RANS) turbulence models offer low-cost and sensible accuracy, they are frequently utilized for bluff bodies’ external aerodynamics investigations (e.g., upwind, crosswind, and shape optimization). However, no firm certainty is made regarding the best model in terms of accuracy and cost. Based on cost and accuracy aspects, four RANS turbulence models were studied, which are Spalart–Allmaras, realizable k-ε, RNG k-ε, and SST k-ω. Ahmed body with a 25° slant angle benchmark case was introduced for this investigation. Two grids were generated to satisfy the near-wall treatment of each turbulence model. All grid settings were proposed and discussed in detail. Fluid-structure analysis was performed on five different planes. Regarding flow field prediction, realizable k-ε and renormalization group (RNG) k-ε models demonstrated a remarkable consistency with experimental data, while Menter’s shear stress transport (SST) k-ω showed a poor agreement. The obtained computational values of drag and lift coefficients were compared with experimental results. All investigated RANS turbulence models had reported results in excellent agreement with experimental drag coefficient values. The SST k-ω model has underestimated lift coefficient value with an error of about −45% with experimental value. Only realizable k-ε and RNG k-ε presented an error <10% for predicting drag and lift coefficients.</div>

Optimal error estimates of a SAV–FEM for the Cahn–Hilliard–Navier–Stokes model

We carry out the optimal error estimates of a scalar auxiliary variable (SAV) based the Euler semi-implicit finite element method for the Cahn–Hilliard–Navier–Stokes (CHNS) system in this paper. A SAV is introduced to reformulate the CHNS system into an equivalent system. We apply the Euler semi-implicit method and finite element method for the temporal and spatial discretizations to obtain a linear and unconditional energy stable scheme. The stability of numerical solutions under different norms and the optimal error estimates for our proposed numerical schemes are also presented. Finally, numerical examples are presented to demonstrate the accuracy of the proposed method, and the discrete energy is dissipated in numerical simulations.

Identification of nonlinear conservation laws for multiphase flow based on Bayesian inversion

Conservation laws of the generic form c_t+f(c)_x=0 play a central role in the mathematical description of various engineering related processes. Identification of an unknown flux function f(c) from observation data in space and time is challenging due to the fact that the solution c(x, t) develops discontinuities in finite time. We explore a Bayesian type of method based on representing the unknown flux f(c) as a Gaussian random process (parameter vector) combined with an iterative ensemble Kalman filter (EnKF) approach to learn the unknown, nonlinear flux function. As a testing ground, we consider displacement of two fluids in a vertical domain where the nonlinear dynamics is a result of a competition between gravity and viscous forces. This process is described by a multidimensional Navier–Stokes model. Subject to appropriate scaling and simplification constraints, a 1D nonlinear scalar conservation law c_t+f(c)_x=0 can be derived with an explicit expression for f(c) for the volume fraction c(x, t). We consider small (noisy) observation data sets in terms of time series extracted at a few fixed positions in space. The proposed identification method is explored for a range of different displacement conditions ranging from pure concave to highly non-convex f(c). No a priori information about the sought flux function is given except a sound choice of smoothness for the a priori flux ensemble. It is demonstrated that the method possesses a strong ability to identify the unknown flux function. The role played by the choice of initial data c_0(x) as well various types of observation data is highlighted.