Numerical simulations of semiconvection

2006 ◽  
Vol 2 (S239) ◽  
pp. 317-319 ◽  
Author(s):  
Guillaume P. Bascoul

AbstractUsing a semiconvective model based on thermohaline convection, we investigate the case of an expanding core of a main-sequence massive star. The numerical simulations at high Prandtl number show a flow consistent with the assumption that a dynamically neutral layer sits between the core and the radiative envelope. More simulations at low Prandtl number are needed to infer scaling laws applicable to astrophysical regimes.

1998 ◽  
Vol 120 (3) ◽  
pp. 758-764 ◽  
Author(s):  
Y. Kamotani ◽  
S. Ostrach

Steady and oscillatory thermocapillary flows of high Prandtl number fluids in the half-zone configuration are analyzed theoretically. Scaling analysis is performed to determine the velocity and length scales of the basic steady flow. The predicted scaling laws agree well with the numerically computed results. The physical mechanism of oscillations is then discussed. It is shown that the deformation of free surface plays an important role for the onset of oscillations in that it alters the main thermocapillary driving force of the flow by changing the temperature field near the hot-corner region. This phenomenon triggers oscillation cycles in which the surface flow undergoes active and slow periods. Based on that concept a surface deformation parameter is derived by scaling analysis. The deformation parameter correlates available data for the onset of oscillations well.


2000 ◽  
Vol 419 ◽  
pp. 325-344 ◽  
Author(s):  
ROBERT M. KERR ◽  
JACKSON R. HERRING

The dependence of the Nusselt number Nu on the Rayleigh Ra and Prandtl Pr number is determined for 104 < Ra < 107 and 0.07 < Pr < 7 using DNS with no-slip upper and lower boundaries and free-slip sidewalls in a 8 × 8 × 2 box. Nusselt numbers, velocity scales and boundary layer thicknesses are calculated. For Nu there are good comparisons with experimental data and scaling laws for all the cases, including Ra2/7 laws at Pr = 0.7 and Pr = 7 and at low Pr, a Ra1/4 regime. Calculations at Pr = 0.3 predict a new Nu ∼ Ra2/7 regime at slightly higher Ra than the Pr = 0.07 calculations reported here and the mercury Pr = 0.025 experiments.


2021 ◽  
Vol 3 (9) ◽  
Author(s):  
Mohammadreza Kasaei ◽  
Ali Ahmadi ◽  
Nuno Lau ◽  
Artur Pereira

AbstractBiped robots are inherently unstable because of their complex kinematics as well as dynamics. Despite many research efforts in developing biped locomotion, the performance of biped locomotion is still far from the expectations. This paper proposes a model-based framework to generate stable biped locomotion. The core of this framework is an abstract dynamics model which is composed of three masses to consider the dynamics of stance leg, torso, and swing leg for minimizing the tracking problems. According to this dynamics model, we propose a modular walking reference trajectories planner which takes into account obstacles to plan all the references. Moreover, this dynamics model is used to formulate the controller as a Model Predictive Control (MPC) scheme which can consider some constraints in the states of the system, inputs, outputs, and also mixed input-output. The performance and the robustness of the proposed framework are validated by performing several numerical simulations using MATLAB. Moreover, the framework is deployed on a simulated torque-controlled humanoid to verify its performance and robustness. The simulation results show that the proposed framework is capable of generating biped locomotion robustly.


2004 ◽  
Vol 16 (5) ◽  
pp. 1746-1757 ◽  
Author(s):  
D. E. Melnikov ◽  
V. M. Shevtsova ◽  
J. C. Legros

2021 ◽  
Author(s):  
Heiko Apel ◽  
Sergiy Vorogushyn ◽  
Mostafa Farrag ◽  
Nguyen Viet Dung ◽  
Melanie Karremann ◽  
...  

&lt;p&gt;Urban flash floods caused by heavy convective precipitation pose an increasing threat to communes world-wide due to the increasing intensity and frequency of convective precipitation caused by a warming atmosphere. Thus, flood risk management plans adapted to the current flood risk but also capable of managing future risks are of high importance. These plans necessarily need model based pluvial flood risk simulations. In an urban environment these simulations have to have a high spatial and temporal resolution in order to site-specific management solutions. Moreover, the effect of the sewer systems needs to be included to achieve realistic inundation simulations, but also to assess the effectiveness of the sewer system and its fitness to future changes in the pluvial hazard. The setup of these models, however, typically requires a large amount of input data, a high degree of modelling expertise, a long time for setting up the model setup and to finally run the simulations. Therefor most communes cannot perform this task.&lt;/p&gt;&lt;p&gt;&amp;#160;In order to provide model-based pluvial urban flood hazard and finally risk assessments for a large number of communes, the model system RIM&lt;em&gt;urban&lt;/em&gt; was developed. The core of the system consists of a simplified raster-based 2D hydraulic model simulating the urban surface inundation in high spatial resolution. The model is implemented on GPUs for massive parallelization. The specific urban hydrology is considered by a capacity-based simulation of the sewer system and infiltration on non-sealed surfaces, and flow routing around buildings. The model thus considers the specific urban hydrological features, but with simplified approaches. Due to these simplifications the model setup can be performed with comparatively low data requirements, which can be covered with open data in most cases. The core data required are a high-resolution DEM, a layer of showing the buildings, and a land use map.&lt;/p&gt;&lt;p&gt;The spatially distributed rainfall input can be derived local precipitation records, or from an analysis of weather radar records of heavy precipitation events. A catalogue of heavy rain storms all over Germany is derived based on radar observations of the past 19 years. This catalogue serves as input for pluvial risk simulations for individual communes in Germany, as well as a catalogue of possible extreme events for the current climate. Future changes in these extreme events will be estimated based on regional climate simulations of a &amp;#916;T (1.5&amp;#176;C, 2&amp;#176;C) warmer world.&lt;/p&gt;&lt;p&gt;RIM&lt;em&gt;urban&lt;/em&gt; simulates the urban inundation caused by these events, as well as the stress on the sewer system. Based on the inundation maps the damage to residential buildings will be estimated and further developed to a pluvial urban flood risk assessment. Because of the comparatively simple model structure and low data demand, the model setup can be easily automatized and transferred to most small to medium sized communes in Europe and even beyond, if the damage estimation is modified. RIM&lt;em&gt;urban&lt;/em&gt; is thus seen as a generally app&amp;#246;licable screening tool for urban pluvial flood risk and a starting point for adapted risk management plans.&lt;/p&gt;


A new scheme of combining the governing equations of thermohaline convection is shown to lead to the following bounds for the complex growth rate p of an arbitrary oscillatory perturbation: | p | 2 < R s σ (Veronis thermohaline configuration), | p | 2 < – R σ (Stern thermohaline configuration), where R and R s are the thermal and the concentration Rayleigh numbers, and σ is the Prandtl number. The analysis is applicable to rotatory thermal and rotatory thermohaline convections for which the corresponding bounds are | p | 2 < T σ 2 (rotatory simple Bénard configuration), | p | 2 < max ( T σ 2 , R s σ) (rotatory Vernois thermohaline configuration), | p | 2 < max ( T σ 2 , – R σ) (rotatory Stern thermohaline configuration), where T is the Taylor number. The above results are valid for all combination of dynamically free and rigid boundaries.


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