A Stable numerical scheme for the cross-diffusion term of near-wall k-ω turbulence models

2019 ◽  
Author(s):  
Yair Mor-Yossef
Keyword(s):  
Numerical Scheme ◽  
Turbulence Models ◽  
Diffusion Term ◽  
Cross Diffusion ◽  
The Cross ◽  
Near Wall

Spatial Pattern of Ratio-Dependent Predator–Prey Model with Prey Harvesting and Cross-Diffusion

2019 ◽  
Vol 29 (03) ◽  
pp. 1950036 ◽  
Author(s):  
R. Sivasamy ◽  
M. Sivakumar ◽  
K. Balachandran ◽  
K. Sathiyanathan
Keyword(s):  
Temporal Dynamics ◽  
Intake Rate ◽  
Diffusion Term ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Nonlinear Harvesting ◽  
Ratio Dependent ◽  
The Cross

This study focuses on the spatial-temporal dynamics of predator–prey model with cross-diffusion where the intake rate of prey is per capita predator according to ratio-dependent functional response and the prey is harvested through nonlinear harvesting strategy. The permanence analysis and local stability analysis of the proposed model without cross-diffusion are analyzed. We derive the conditions for the appearance of diffusion-driven instability and global stability of the considered model. Also the parameter space for Turing region is specified by keeping the cross-diffusion coefficient as one of the crucial parameters. Numerical simulations are given to justify the proposed theoretical results and to show that the cross-diffusion term plays a significant role in the pattern formation.

scholarly journals A meeting point of entropy and bifurcations in cross-diffusion herding

2016 ◽  
Vol 28 (2) ◽  
pp. 317-356 ◽  
Author(s):  
ANSGAR JÜNGEL ◽  
CHRISTIAN KUEHN ◽  
LARA TRUSSARDI
Keyword(s):  
Gradient Flow ◽  
Stationary Solutions ◽  
Steady States ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
System Modelling ◽  
Local Bifurcation ◽  
Diffusion Term ◽  
Cross Diffusion ◽  
The Cross

A cross-diffusion system modelling the information herding of individuals is analysed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state of the individuals. The cross-diffusion term may stabilize or destabilize the system. Furthermore, it allows for a formal gradient-flow or entropy structure. Exploiting this structure, the global-in-time existence of weak solutions and the exponential decay to the constant steady state is proved in certain parameter regimes. This approach does not extend to all parameters. We investigate local bifurcations from homogeneous steady states analytically to determine whether this defines the validity boundary. This analysis shows that generically there is a gap in the parameter regime between the entropy approach validity and the first local bifurcation. Next, we use numerical continuation methods to track the bifurcating non-homogeneous steady states globally and to determine non-trivial stationary solutions related to herding behaviour. In summary, we find that the main boundaries in the parameter regime are given by the first local bifurcation point, the degeneracy of the diffusion matrix and a certain entropy decay validity condition. We study several parameter limits analytically as well as numerically, with a focus on the role of changing a linear damping parameter as well as a parameter controlling the cross-diffusion. We suggest that our paradigm of comparing bifurcation-generated obstructions to the parameter validity of global-functional methods could also be of relevance for many other models beyond the one studied here.

scholarly journals Turbulence model performance for ventilation components pressure losses

2021 ◽  
Author(s):  
Karsten Tawackolian ◽  
Martin Kriegel
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Pressure Loss ◽  
Low Reynolds Number ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Test Case ◽  
Pressure Losses ◽  
Loss Coefficients ◽  
Near Wall

AbstractThis study looks to find a suitable turbulence model for calculating pressure losses of ventilation components. In building ventilation, the most relevant Reynolds number range is between 3×104 and 6×105, depending on the duct dimensions and airflow rates. Pressure loss coefficients can increase considerably for some components at Reynolds numbers below 2×105. An initial survey of popular turbulence models was conducted for a selected test case of a bend with such a strong Reynolds number dependence. Most of the turbulence models failed in reproducing this dependence and predicted curve progressions that were too flat and only applicable for higher Reynolds numbers. Viscous effects near walls played an important role in the present simulations. In turbulence modelling, near-wall damping functions are used to account for this influence. A model that implements near-wall modelling is the lag elliptic blending k-ε model. This model gave reasonable predictions for pressure loss coefficients at lower Reynolds numbers. Another example is the low Reynolds number k-ε turbulence model of Wilcox (LRN). The modification uses damping functions and was initially developed for simulating profiles such as aircraft wings. It has not been widely used for internal flows such as air duct flows. Based on selected reference cases, the three closure coefficients of the LRN model were adapted in this work to simulate ventilation components. Improved predictions were obtained with new coefficients (LRNM model). This underlined that low Reynolds number effects are relevant in ventilation ductworks and give first insights for suitable turbulence models for this application. Both the lag elliptic blending model and the modified LRNM model predicted the pressure losses relatively well for the test case where the other tested models failed.

scholarly journals Performance of Turbulence Models and Near-Wall Treatments in Discrete Jet Film Cooling Simulations

1998 ◽  
Author(s):  
Jeffrey D. Ferguson ◽  
Dibbon K. Walters ◽  
James H. Leylek
Keyword(s):  
Experimental Data ◽  
Film Cooling ◽  
Turbulence Models ◽  
Viscous Sublayer ◽  
Reynolds Stress Model ◽  
Quality Data ◽  
Wall Functions ◽  
First Time ◽  
Near Wall ◽  
Non Equilibrium

For the first time in the open literature, code validation quality data and a well-tested, highly reliable computational methodology are employed to isolate the true performance of seven turbulence treatments in discrete jet film cooling. The present research examines both computational and high quality experimental data for two length-to-diameter ratios of a row of streamwise injected, cylindrical film holes. These two cases are used to document the performance of the following turbulence treatments: 1) standard k-ε model with generalized wall functions; 2) standard k-ε model with non-equilibrium wall functions: 3) Renormalization Group k-ε (RNG) model with generalized wall functions; 4) RNG model with non-equilibrium wall functions: 51 standard k-ε model with two-layer turbulence wall treatment; 6) Reynolds Stress Model (RSM) with generalized wall functions; and 7) RSM with non-equilibrium wall functions. Overall, the standard k-ε turbulence model with the two-layer near-wall treatment, which resolves the viscous sublayer, produces results that are more consistent with experimental data.

scholarly journals MHDSTS: a new explicit numerical scheme for simulations of partially ionised solar plasma

2018 ◽  
Vol 615 ◽  
pp. A67 ◽  
Author(s):  
P. A. González-Morales ◽  
E. Khomenko ◽  
T. P. Downes ◽  
A. de Vicente
Keyword(s):  
Numerical Scheme ◽  
Operator Splitting ◽  
Conservation Equation ◽  
Ambipolar Diffusion ◽  
Point Of View ◽  
Integration Time ◽  
Solar Photosphere ◽  
Time Step ◽  
Diffusion Term ◽  
Fluid Approximation

The interaction of plasma with magnetic field in the partially ionised solar atmosphere is frequently modelled via a single-fluid approximation, which is valid for the case of a strongly coupled collisional media, such as solar photosphere and low chromosphere. Under the single-fluid formalism the main non-ideal effects are described by a series of extra terms in the generalised induction equation and in the energy conservation equation. These effects are: Ohmic diffusion, ambipolar diffusion, the Hall effect, and the Biermann battery effect. From the point of view of the numerical solution of the single-fluid equations, when ambipolar diffusion or Hall effects dominate can introduce severe restrictions on the integration time step and can compromise the stability of the numerical scheme. In this paper we introduce two numerical schemes to overcome those limitations. The first of them is known as super time-stepping (STS) and it is designed to overcome the limitations imposed when the ambipolar diffusion term is dominant. The second scheme is called the Hall diffusion scheme (HDS) and it is used when the Hall term becomes dominant. These two numerical techniques can be used together by applying Strang operator splitting. This paper describes the implementation of the STS and HDS schemes in the single-fluid code MANCHA3D. The validation for each of these schemes is provided by comparing the analytical solution with the numerical one for a suite of numerical tests.

scholarly journals Rigorous Derivation of Population Cross-Diffusion Systems from Moderately Interacting Particle Systems

2021 ◽  
Vol 31 (6) ◽  
Author(s):  
Li Chen ◽  
Esther S. Daus ◽  
Alexandra Holzinger ◽  
Ansgar Jüngel
Keyword(s):  
Interacting Particle Systems ◽  
Mean Field ◽  
Strong Solutions ◽  
Particle Systems ◽  
Mean Field Limit ◽  
Diffusion Term ◽  
Small Initial Data ◽  
Dirac Delta ◽  
Cross Diffusion ◽  
Diffusion Systems

AbstractPopulation cross-diffusion systems of Shigesada–Kawasaki–Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion term in the stochastic model depends nonlinearly on the interactions between the individuals, and the drift term is the gradient of the environmental potential. In the first step, the mean-field limit leads to an intermediate nonlocal model. The local cross-diffusion system is derived in the second step in a moderate scaling regime, when the interaction potentials approach the Dirac delta distribution. The global existence of strong solutions to the intermediate and the local diffusion systems is proved for sufficiently small initial data. Furthermore, numerical simulations on the particle level are presented.

Reynolds Number Effect on the Flow Demeanorin a Vertical Circular Free Turbulent Jet with Cross Flow

2021 ◽  
Vol 409 ◽  
pp. 158-178
Author(s):  
Abdelkader Feddal ◽  
Abbes Azzi ◽  
Ahmed Zineddine Dellil
Keyword(s):  
Reynolds Number ◽  
Cross Flow ◽  
Turbulence Models ◽  
Turbulent Jets ◽  
Turbulent Jet ◽  
Low Velocity ◽  
Transverse Current ◽  
Ansys Cfx ◽  
The Cross ◽  
Two Jets

This paper deals with studying numerically two circular turbulent jets impinging on a flat surface with a low velocity cross flow by using ANSYS CFX 16.2, with the aim of proving the effect ofReynolds number on the flow demeanor in a vertical circular free turbulent jet with cross flow. Five turbulence models of the RANS (Reynolds Averaged Navier–Stokes) approach were tested and the k -ω SST model was chosen to validate CFD results with the experimental data. Average velocity profiles, velocity and turbulent kinetic energy contours and streamlines are presented for four case configurations. In the first three cases, the following parameters have been varied: Reynolds number at the level of the two jets ( ), wind velocity at the level of the cross-flow ( ), and the distance between the two jets (S = 45mm, 90mm and 135mm). In the last case, a new configuration of the phenomenon not yet studied so far was treated, where horizontal cross-flows were introduced from both sides in order to simulate gusts of wind disrupting a VSTOL aircraft which tries to operate close to the ground. This case was carried out for Reynolds number based on the crossflow of 4 104, 10 104 and 20 104 .The numerical results obtained show that the deflection of the jets is minimal when the Reynolds number at the level of the jets is greater than that of the cross-flow. The increase of Reynolds number at the level of the cross-flow reveals a significant deviation of the two jets with an intensity which always remains less for the second jet. As for the space parameter between the two jets, it turns out that the fact of further spacing the two jets makes the first jet even more vulnerable and leads to a greater deflection. Finally, the simulation of the wind gusts from the front and the back caused a zone of turbulence which resulted from a form of "interlacing" of the two jets under the effect of the transverse current imposed by the two sides.

Improved Prediction of Turbomachinery Flows Using Near-Wall Reynolds-Stress Model

2001 ◽  
Vol 124 (1) ◽  
pp. 86-99 ◽  
Author(s):  
G. A. Gerolymos ◽  
J. Neubauer ◽  
V. C. Sharma ◽  
I. Vallet
Keyword(s):  
Experimental Data ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flow Equations ◽  
Near Wall

In this paper an assessment of the improvement in the prediction of complex turbomachinery flows using a new near-wall Reynolds-stress model is attempted. The turbulence closure used is a near-wall low-turbulence-Reynolds-number Reynolds-stress model, that is independent of the distance-from-the-wall and of the normal-to-the-wall direction. The model takes into account the Coriolis redistribution effect on the Reynolds-stresses. The five mean flow equations and the seven turbulence model equations are solved using an implicit coupled OΔx3 upwind-biased solver. Results are compared with experimental data for three turbomachinery configurations: the NTUA high subsonic annular cascade, the NASA_37 rotor, and the RWTH 1 1/2 stage turbine. A detailed analysis of the flowfield is given. It is seen that the new model that takes into account the Reynolds-stress anisotropy substantially improves the agreement with experimental data, particularily for flows with large separation, while being only 30 percent more expensive than the k−ε model (thanks to an efficient implicit implementation). It is believed that further work on advanced turbulence models will substantially enhance the predictive capability of complex turbulent flows in turbomachinery.

scholarly journals Dynamics and asymptotic profiles of endemic equilibrium for two frequency-dependent SIS epidemic models with cross-diffusion

2018 ◽  
Vol 31 (1) ◽  
pp. 26-56 ◽  
Author(s):  
HUICONG LI ◽  
RUI PENG ◽  
TIAN XIANG
Keyword(s):  
Infectious Disease ◽  
Total Population ◽  
Initial Boundary ◽  
Endemic Equilibrium ◽  
Diffusion Term ◽  
Frequency Dependent ◽  
Susceptible Population ◽  
Cross Diffusion ◽  
Special Cases ◽  
Globally Stable

This paper is concerned with two frequency-dependent susceptible–infected–susceptible epidemic reaction–diffusion models in heterogeneous environment, with a cross-diffusion term modelling the effect that susceptible individuals tend to move away from higher concentration of infected individuals. It is first shown that the corresponding Neumann initial-boundary value problem in an n-dimensional bounded smooth domain possesses a unique global classical solution which is uniformly in-time bounded regardless of the strength of the cross-diffusion and the spatial dimension n. It is further shown that, even in the presence of cross-diffusion, the models still admit threshold-type dynamics in terms of the basic reproduction number $\mathcal {R}_0$ – i.e. the unique disease-free equilibrium is globally stable if $\mathcal {R}_0\lt1$, while if $\mathcal {R}_0\gt1$, the disease is uniformly persistent and there is an endemic equilibrium (EE), which is globally stable in some special cases with weak chemotactic sensitivity. Our results on the asymptotic profiles of EE illustrate that restricting the motility of susceptible population may eliminate the infectious disease entirely for the first model with constant total population but fails for the second model with varying total population. In particular, this implies that such cross-diffusion does not contribute to the elimination of the infectious disease modelled by the second one.

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