scholarly journals Moving and reactive boundary conditions in moving-mesh hydrodynamics

2020 ◽  
Vol 494 (4) ◽  
pp. 4616-4626 ◽  
Author(s):  
Logan J Prust
Keyword(s):  
Boundary Conditions ◽  
Moving Boundary ◽  
Initial Conditions ◽  
Moving Boundaries ◽  
Moving Mesh ◽  
Test Cases ◽  
Conserved Quantities ◽  
Common Envelope ◽  
Gravitational Forces ◽  
Spherical Boundary

ABSTRACT We outline the methodology of implementing moving boundary conditions into the moving-mesh code manga. The motion of our boundaries is reactive to hydrodynamic and gravitational forces. We discuss the hydrodynamics of a moving boundary as well as the modifications to our hydrodynamic and gravity solvers. Appropriate initial conditions to accurately produce a boundary of arbitrary shape are also discussed. Our code is applied to several test cases, including a Sod shock tube, a Sedov–Taylor blast wave, and a supersonic wind on a sphere. We show the convergence of conserved quantities in our simulations. We demonstrate the use of moving boundaries in astrophysical settings by simulating a common envelope phase in a binary system, in which the companion object is modelled by a spherical boundary. We conclude that our methodology is suitable to simulate astrophysical systems using moving and reactive boundary conditions.

scholarly journals Common envelope evolution on a moving mesh

2019 ◽  
Vol 486 (4) ◽  
pp. 5809-5818 ◽  
Author(s):  
Logan J Prust ◽  
Philip Chang
Keyword(s):  
Dynamic Range ◽  
Equations Of State ◽  
Orbital Motion ◽  
Initial Conditions ◽  
Stellar Structure ◽  
Moving Mesh ◽  
Multiple Time ◽  
Recombination Energy ◽  
Common Envelope ◽  
Red Giant

Abstract We outline the methodology of simulating common envelope evolution (CEE) with the moving-mesh code manga. We extend manga to include multiple time-steps. This provides substantial speedups for problems with large dynamic range. We describe the implementation of realistic equations of state relevant in stellar structure and the generation of suitable initial conditions. We then carry out two example simulations of a 2 M⊙ red giant with a 0.36 M⊙ core and a 1 M⊙ companion undergoing CEE for 240 days. In one simulation the red giant is set into corotation with the orbital motion and in the other it is non-rotating. We find that the separation between the companion and red giant core shrinks from 52 R⊙ to 3.6 R⊙ and 3.2 R⊙, respectively, ending with an eccentricity of 0.1. We also find that 66 and 63 per cent of the envelope mass is ejected. This is higher than in many previous works. Several reasons for this are discussed. These include our inclusion of recombination energy. Our simulations show that putting giants in corotation increases the fraction of mass ejected from the system and results in a larger final orbital separation. We conclude that the entire envelope of the red giant might be ejected during the plunge phase of CEE in this region of parameter space.

scholarly journals Mathematical Modeling of Release Kinetics from Supramolecular Drug Delivery Systems

Pharmaceutics ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 140 ◽  
Author(s):  
Constantin Mircioiu ◽  
Victor Voicu ◽  
Valentina Anuta ◽  
Andra Tudose ◽  
Christian Celia ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Moving Boundary ◽  
Initial Conditions ◽  
Integral Transformation ◽  
Release Kinetics ◽  
Separation Of Variables ◽  
Transformation Method ◽  
Mathematical Methods ◽  
Important Place ◽  
First Choice

Embedding of active substances in supramolecular systems has as the main goal to ensure the controlled release of the active ingredients. Whatever the final architecture or entrapment mechanism, modeling of release is challenging due to the moving boundary conditions and complex initial conditions. Despite huge diversity of formulations, diffusion phenomena are involved in practically all release processes. The approach in this paper starts, therefore, from mathematical methods for solving the diffusion equation in initial and boundary conditions, which are further connected with phenomenological conditions, simplified and idealized in order to lead to problems which can be analytically solved. Consequently, the release models are classified starting from the geometry of diffusion domain, initial conditions, and conditions on frontiers. Taking into account that practically all solutions of the models use the separation of variables method and integral transformation method, two specific applications of these methods are included. This paper suggests that “good modeling practice” of release kinetics consists essentially of identifying the most appropriate mathematical conditions corresponding to implied physicochemical phenomena. However, in most of the cases, models can be written but analytical solutions for these models cannot be obtained. Consequently, empiric models remain the first choice, and they receive an important place in the review.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

DYNAMICS OF THERMAL LOSSES BY CONVECTION AND RADIATION OF THE SPHERICAL HEAT ACCUMULATOR OF SOLAR PLANTS

2020 ◽  
Vol 4 (41) ◽  
pp. 57-62
Author(s):  
SHAVKAT KLYCHEV ◽  
◽  
BAKHRAMOV SAGDULLA ◽  
VALERIY KHARCHENKO ◽  
VLADIMIR PANCHENKO ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Heat Loss ◽  
Initial Conditions ◽  
Water System ◽  
Heat Losses ◽  
Research Purpose ◽  
Heat Accumulator ◽  
Water Heaters ◽  
Intrinsic Radiation ◽  
Over Time

There are needed energy (heat) accumulators to increase the efficiency of solar installations, including solar collectors (water heaters, air heaters, dryers). One of the tasks of designing heat accumulators is to ensure its minimal heat loss. The article considers the problem of determining the distribution of temperatures and heat losses by convection and radiation of the heat insulation-accumulating body (water) system for a ball heat accumulator under symmetric boundary conditions. The problem is solved numerically according to the program developed on the basis of the proposed «gap method». (Research purpose) The research purpose is in determining heat losses by convection and radiation of a two-layer ball heat accumulator with symmetric boundary conditions. (Materials and methods) Authors used the Fourier heat equation for spherical bodies. The article presents the determined boundary and initial conditions for bodies and their surfaces. (Results and discussion) The thickness of the insulation and the volume of the heat accumulator affect the dynamics and values of heat loss. The effect of increasing the thickness of the thermal insulation decreases with increasing its thickness, starting with a certain volume of the heat accumulator or with R > 0.3 meters, the heat losses change almost linearly over time. The dynamics of heat loss decreases with increasing shelf life, but the losses remain large. (Conclusions) Authors have developed a method and program for numerical calculation of heat loss and temperature over time in a spherical two-layer heat accumulator with symmetric boundary conditions, taking into account both falling and intrinsic radiation. The proposed method allows to unify the boundary conditions between contacting bodies.

scholarly journals Solving nonlinear third-order three-point boundary value problems by boundary shape functions methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ji Lin ◽  
Yuhui Zhang ◽  
Chein-Shan Liu
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Initial Conditions ◽  
Boundary Value ◽  
Accurate Solution ◽  
Point Boundary ◽  
Third Order ◽  
Boundary Shape ◽  
Free Function ◽  
New Algorithms

AbstractFor nonlinear third-order three-point boundary value problems (BVPs), we develop two algorithms to find solutions, which automatically satisfy the specified three-point boundary conditions. We construct a boundary shape function (BSF), which is designed to automatically satisfy the boundary conditions and can be employed to develop new algorithms by assigning two different roles of free function in the BSF. In the first algorithm, we let the free functions be complete functions and the BSFs be the new bases of the solution, which not only satisfy the boundary conditions automatically, but also can be used to find solution by a collocation technique. In the second algorithm, we let the BSF be the solution of the BVP and the free function be another new variable, such that we can transform the BVP to a corresponding initial value problem for the new variable, whose initial conditions are given arbitrarily and terminal values are determined by iterations; hence, we can quickly find very accurate solution of nonlinear third-order three-point BVP through a few iterations. Numerical examples confirm the performance of the new algorithms.

scholarly journals Simulation of MASPn Experiments in MISTRA Test Facility with COCOSYS Code

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Mantas Povilaitis ◽  
Egidijus Urbonavičius
Keyword(s):  
Boundary Conditions ◽  
Nuclear Power ◽  
Power Plants ◽  
Volume Fraction ◽  
Characteristic Length ◽  
Initial Conditions ◽  
Test Facility ◽  
Work Package ◽  
Acceptable Agreement

An issue of the stratified atmospheres in the containments of nuclear power plants is still unresolved; different experiments are performed in the test facilities like TOSQAN and MISTRA. MASPn experiments belong to the spray benchmark, initiated in the containment atmosphere mixing work package of the SARNET network. The benchmark consisted of MASP0, MASP1 and MASP2 experiments. Only the measured depressurisation rates during MASPn were available for the comparison with calculations. When the analysis was performed, the boundary conditions were not clearly defined therefore most of the attention was concentrated on MASP0 simulation in order to develop the nodalisation scheme and define the initial and boundary conditions. After achieving acceptable agreement with measured depressurisation rate, simulations of MASP1 and MASP2 experiments were performed to check the influence of sprays. The paper presents developed nodalisation scheme of MISTRA for the COCOSYS code and the results of analyses. In the performed analyses, several parameters were considered: initial conditions, loss coefficient of the junctions, initial gradients of temperature and steam volume fraction, and characteristic length of structures. Parametric analysis shows that in the simulation the heat losses through the external walls behind the lower condenser installed in the MISTRA facility determine the long-term depressurisation rate.

scholarly journals Automated Search-Based Robustness Testing for Autonomous Vehicle Software

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Kevin M. Betts ◽  
Mikel D. Petty
Keyword(s):  
Monte Carlo ◽  
Performance Metrics ◽  
Initial Conditions ◽  
Autonomous Vehicle ◽  
Vehicle Control ◽  
Test Case ◽  
Test Cases ◽  
Control Software ◽  
Robustness Testing ◽  
Testing Techniques

Autonomous systems must successfully operate in complex time-varying spatial environments even when dealing with system faults that may occur during a mission. Consequently, evaluating the robustness, or ability to operate correctly under unexpected conditions, of autonomous vehicle control software is an increasingly important issue in software testing. New methods to automatically generate test cases for robustness testing of autonomous vehicle control software in closed-loop simulation are needed. Search-based testing techniques were used to automatically generate test cases, consisting of initial conditions and fault sequences, intended to challenge the control software more than test cases generated using current methods. Two different search-based testing methods, genetic algorithms and surrogate-based optimization, were used to generate test cases for a simulated unmanned aerial vehicle attempting to fly through an entryway. The effectiveness of the search-based methods in generating challenging test cases was compared to both a truth reference (full combinatorial testing) and the method most commonly used today (Monte Carlo testing). The search-based testing techniques demonstrated better performance than Monte Carlo testing for both of the test case generation performance metrics: (1) finding the single most challenging test case and (2) finding the set of fifty test cases with the highest mean degree of challenge.

scholarly journals Impact of physical parameterizations and initial conditions on simulated atmospheric transport and CO<sub>2</sub> mole fractions in the US Midwest

2018 ◽  
Vol 18 (20) ◽  
pp. 14813-14835 ◽  
Author(s):  
Liza I. Díaz-Isaac ◽  
Thomas Lauvaux ◽  
Kenneth J. Davis
Keyword(s):  
Boundary Layer ◽  
Wind Speed ◽  
Boundary Conditions ◽  
Planetary Boundary Layer ◽  
Initial Conditions ◽  
Atmospheric Transport ◽  
Atmospheric Co2 ◽  
The Us ◽  
Physics Parameterizations ◽  
Physical Parameterizations

Abstract. Atmospheric transport model errors are one of the main contributors to the uncertainty affecting CO2 inverse flux estimates. In this study, we determine the leading causes of transport errors over the US upper Midwest with a large set of simulations generated with the Weather Research and Forecasting (WRF) mesoscale model. The various WRF simulations are performed using different meteorological driver datasets and physical parameterizations including planetary boundary layer (PBL) schemes, land surface models (LSMs), cumulus parameterizations and microphysics parameterizations. All the different model configurations were coupled to CO2 fluxes and lateral boundary conditions from the CarbonTracker inversion system to simulate atmospheric CO2 mole fractions. PBL height, wind speed, wind direction, and atmospheric CO2 mole fractions are compared to observations during a month in the summer of 2008, and statistical analyses were performed to evaluate the impact of both physics parameterizations and meteorological datasets on these variables. All of the physical parameterizations and the meteorological initial and boundary conditions contribute 3 to 4 ppm to the model-to-model variability in daytime PBL CO2 except for the microphysics parameterization which has a smaller contribution. PBL height varies across ensemble members by 300 to 400 m, and this variability is controlled by the same physics parameterizations. Daily PBL CO2 mole fraction errors are correlated with errors in the PBL height. We show that specific model configurations systematically overestimate or underestimate the PBL height averaged across the region with biases closely correlated with the choice of LSM, PBL scheme, and cumulus parameterization (CP). Domain average PBL wind speed is overestimated in nearly every model configuration. Both planetary boundary layer height (PBLH) and PBL wind speed biases show coherent spatial variations across the Midwest, with PBLH overestimated averaged across configurations by 300–400 m in the west, and PBL winds overestimated by about 1 m s−1 on average in the east. We find model configurations with lower biases averaged across the domain, but no single configuration is optimal across the entire region and for all meteorological variables. We conclude that model ensembles that include multiple physics parameterizations and meteorological initial conditions are likely to be necessary to encompass the atmospheric conditions most important to the transport of CO2 in the PBL, but that construction of such an ensemble will be challenging due to ensemble biases that vary across the region.

scholarly journals Validation of an ocean shelf model for the prediction of mixed-layer properties in the Mediterranean Sea west of Sardinia

Ocean Science ◽  
2017 ◽  
Vol 13 (2) ◽  
pp. 235-257 ◽  
Author(s):  
Reiner Onken
Keyword(s):  
Boundary Conditions ◽  
Mixed Layer ◽  
Initial Conditions ◽  
Mixed Layer Depth ◽  
Vertical Mixing ◽  
Global Ocean ◽  
Wave Number ◽  
Surface Boundary ◽  
Regional Ocean Modeling System ◽  
The Mediterranean

Abstract. The Regional Ocean Modeling System (ROMS) has been employed to explore the sensitivity of the forecast skill of mixed-layer properties to initial conditions, boundary conditions, and vertical mixing parameterisations. The initial and lateral boundary conditions were provided by the Mediterranean Forecasting System (MFS) or by the MERCATOR global ocean circulation model via one-way nesting; the initial conditions were additionally updated through the assimilation of observations. Nowcasts and forecasts from the weather forecast models COSMO-ME and COSMO-IT, partly melded with observations, served as surface boundary conditions. The vertical mixing was parameterised by the GLS (generic length scale) scheme Umlauf and Burchard (2003) in four different set-ups. All ROMS forecasts were validated against the observations which were taken during the REP14-MED survey to the west of Sardinia. Nesting ROMS in MERCATOR and updating the initial conditions through data assimilation provided the best agreement of the predicted mixed-layer properties with the time series from a moored thermistor chain. Further improvement was obtained by the usage of COSMO-ME atmospheric forcing, which was melded with real observations, and by the application of the k-ω vertical mixing scheme with increased vertical eddy diffusivity. The predicted temporal variability of the mixed-layer temperature was reasonably well correlated with the observed variability, while the modelled variability of the mixed-layer depth exhibited only agreement with the observations near the diurnal frequency peak. For the forecasted horizontal variability, reasonable agreement was found with observations from a ScanFish section, but only for the mesoscale wave number band; the observed sub-mesoscale variability was not reproduced by ROMS.

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