Boundary Of Computational Domain Research Articles

Physics-informed boundary integral networks (PIBI-Nets): A data-driven approach for solving partial differential equations

Partial differential equations (PDEs) are widely used to describe relevant phenomena in dynamical systems. In real-world applications, we commonly need to combine formal PDE models with (potentially noisy) observations. This is especially relevant in settings where we lack information about boundary or initial conditions, or where we need to identify unknown model parameters. In recent years, Physics-Informed Neural Networks (PINNs) have become a popular tool for this kind of problems. In high-dimensional settings, however, PINNs often suffer from computational problems because they usually require dense collocation points over the entire computational domain. To address this problem, we present Physics-Informed Boundary Integral Networks (PIBI-Nets) as a data-driven approach for solving PDEs in one dimension less than the original problem space. PIBI-Nets only require points at the computational domain boundary, while still achieving highly accurate results. Moreover, PIBI-Nets clearly outperform PINNs in several practical settings. Exploiting elementary properties of fundamental solutions of linear differential operators, we present a principled and simple way to handle point sources in inverse problems. We demonstrate the excellent performance of PIBI-Nets for the Laplace and Poisson equations, both on artificial datasets and within a real-world application concerning the reconstruction of groundwater flows.

First results of EAST edge modeling with SOLPS‐ITER 3.2.0 on Extended Grid

AbstractThe processes in far scrape‐off layer (SOL) and the plasma interaction with the first‐wall (FW) elements may notably affect the tokamak discharge, since they define fuel and impurity recycling, material erosion and redeposition, wall surface heating, etc. For a long time, the far SOL description in most plasma edge transport codes was insufficient or absent at all, and so particle and heat fluxes onto the FW (except divertor plates) were out of consideration. Recently some codes, for example, SOLEDGE and SOLPS‐ITER are upgraded allowing for the extension of the computational grid up to real walls and for corresponding account of the vacuum vessel shape and all in‐vessel elements. The new release of SOLPS‐ITER (the version 3.2.0) required a development of a new code data structure and new approach to numerical approximation of fluid equations compatible with unstructured non‐orthogonal computational grid. Intensive testing of the new code in different conditions is still required. In the present contribution, such a testing is performed for the EAST disconnected double null (DDN) L‐mode discharge. For the first time, the SOLPS‐ITER 3.2.0 modeling results with drifts and currents turned on are presented, and a comparison to former SOLPS‐ITER version (3.0.8) is performed. The far SOL transport and its effects on the discharge performance are studied by comparing the computational results obtained on several meshes which differ by their width in equatorial midplane. A single null (SN) one (with mesh width limited by distance to the secondary separatrix) was examined versus two DDN meshes (one with actual and one with artificially extended targets to make mesh wider) and a true unstructured (the widest) mesh. The notable difference in results obtained on different meshes appears in those places where plasma density does not vanishes at the computational domain boundaries. For the cases on true unstructured (the widest) mesh, the particle and heat fluxes onto central column, limiters, far SOL part of targets, dome umbrella and other EAST far SOL in‐vessel structures are calculated for the first time by SOLPS‐ITER, allowing assessment of the plasma interaction with those surfaces.

IKA-FLOW : A Flexible Body Overset Mesh Implementation for Fish Swimming

Simulation of inertial aquatic swimmers requires fluid structure interactions with temporal body geometry deformation. In practice, his results in a change of the computational domain boundaries that represent the ”swimmer.” These simulations are traditionally done sing body-fitted mesh and mesh morphing methods, but have drawbacks of negative cell volumes and small time-steps to account for the complex swimming motion. In contrast, the overset mesh method, also provided by OpenFOAM®, overcomes most of the drawbacks of the mesh morphing method at the expense of interpolation error. The current OpenFOAM® overset motion library only supports rigid body motion and cannot be used to resolve a body undergoing undulation. A modified motion solver is presented that allows for the complex mesh motion of an overset mesh for four body-caudal fin (BCF) virtual swimmers. The results of this solver are compared with published data of body-fitted meshes. The effect of different simulation parameters (including number of solving iterations, time delay, and temporal resolution) is investigated. Additionally, a novel simulation and comparison of the Ostraciiform locomotion mode with Anguilliform, Carangiform, and Thunniform modes are made investigating the wake, drag and lift. It is concluded that fish undulation has a marked effect on reducing lift generation. Lastly, a comparison of turbulence models (Spalart-Allmaras, k − ω SST, and k − kL − ω) at multiple Reynolds numbers shows that all three models have similar performance at lower Reynolds numbers but diverge at higher numbers.

Fast High Order Algorithm for Three-Dimensional Helmholtz Equation Involving Impedance Boundary Condition with Large Wave Numbers

Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundary value problems. Finite difference method is widely applied to solving these problems due to its ease of use. However, when the wave number is large, the pollution effects are still a major difficulty in obtaining accurate numerical solutions. We develop a fast algorithm for solving three-dimensional Helmholtz boundary problems with large wave numbers. The boundary of computational domain is discrete based on high-order compact difference scheme. Using the properties of the tensor product and the discrete Fourier sine transform method, the original problem is solved by splitting it into independent small tridiagonal subsystems. Numerical examples with impedance boundary conditions are used to verify the feasibility and accuracy of the proposed algorithm. Results demonstrate that the algorithm has a fourth- order convergence in and -norms, and costs less CPU calculation time and random access memory.

Schwarz methods by domain truncation

Schwarz methods use a decomposition of the computational domain into subdomains and need to impose boundary conditions on the subdomain boundaries. In domain truncation one restricts the unbounded domain to a bounded computational domain and must also put boundary conditions on the computational domain boundaries. In both fields there are vast bodies of literature and research is very active and ongoing. It turns out to be fruitful to think of the domain decomposition in Schwarz methods as a truncation of the domain onto subdomains. Seminal precursors of this fundamental idea are papers by Hagstrom, Tewarson and Jazcilevich (1988), Després (1990) and Lions (1990). The first truly optimal Schwarz method that converges in a finite number of steps was proposed by Nataf (1993), and used precisely transparent boundary conditions as transmission conditions between subdomains. Approximating these transparent boundary conditions for fast convergence of Schwarz methods led to the development of optimized Schwarz methods – a name that has become common for Schwarz methods based on domain truncation. Compared to classical Schwarz methods, which use simple Dirichlet transmission conditions and have been successfully used in a wide range of applications, optimized Schwarz methods are much less well understood, mainly due to their more sophisticated transmission conditions.A key application of Schwarz methods with such sophisticated transmission conditions turned out to be time-harmonic wave propagation problems, because classical Schwarz methods simply do not work in this case. The past decade has given us many new Schwarz methods based on domain truncation. One review from an algorithmic perspective (Gander and Zhang 2019) showed the equivalence of many of these new methods to optimized Schwarz methods. The analysis of optimized Schwarz methods, however, is lagging behind their algorithmic development. The general abstract Schwarz framework cannot be used for the analysis of these methods, and thus there are many open theoretical questions about their convergence. Just as for practical multigrid methods, Fourier analysis has been instrumental for understanding the convergence of optimized Schwarz methods and for tuning their transmission conditions. Similar to local Fourier mode analysis in multigrid, the unbounded two-subdomain case is used as a model for Fourier analysis of optimized Schwarz methods due to its simplicity. Many aspects of the actual situation,e.g.boundary conditions of the original problem and the number of subdomains, were thus neglected in the unbounded two-subdomain analysis. While this gave important insight, new phenomena beyond the unbounded two-subdomain models were discovered.This present situation is the motivation for our survey: to give a comprehensive review and precise exploration of convergence behaviours of optimized Schwarz methods based on Fourier analysis, taking into account the original boundary conditions, many-subdomain decompositions and layered media. We consider as our model problem the operator$-\Delta + \eta $in the diffusive case$\eta>0$(screened Laplace equation) or the oscillatory case$\eta <0$(Helmholtz equation), in order to show the fundamental difference in behaviour of Schwarz solvers for these problems. The transmission conditions we study include the lowest-order absorbing conditions (Robin), and also more advanced perfectly matched layers (PMLs), both developed first for domain truncation. Our intensive work over the last two years on this review has led to several new results presented here for the first time: in the bounded two-subdomain analysis for the Helmholtz equation, we see strong influence of the original boundary conditions imposed on the global problem on the convergence factor of the Schwarz methods, and the asymptotic convergence factors with small overlap can differ from the unbounded two-subdomain analysis. In the many-subdomain analysis, we find the scaling with the number of subdomains,e.g.when the subdomain size is fixed, robust convergence of the double-sweep Schwarz method for the free-space wave problem, either with fixed overlap and zeroth-order Taylor conditions or with a logarithmically growing PML, and we find that Schwarz methods with PMLs work like smoothers that converge faster for higher Fourier frequencies; in particular, for the free-space wave problem, plane waves (in the error) passing through interfaces at a right angle converge more slowly. In addition to our main focus on analysis in Sections 2 and 3, we start in Section 1 with an expository historical introduction to Schwarz methods, and in Section 4 we give a brief interpretation of the recently proposed optimal Schwarz methods for decompositions with cross-points from the viewpoint of transmission conditions. We conclude in Section 5 with a summary of open research problems. In Appendix A we provide a Matlab program for a block LU form of an optimal Schwarz method with cross-points, and in Appendix B we give the Maple program for the two-subdomain Fourier analysis.

Комбинированный бессеточный метод решения смешанных краевых задач при моделировании потенциальных физических полей

Приведено описание комбинированного бессеточного метода решения смешанных краевых задач для уравнения Лапласа, возникающих при анализе потенциальных физических полей в однородных средах. Решение найдено с использованием бессеточных методов фундаментальных решений и Монте-Карло. Выполнена модификация этих методов с учетом особенностей, связанных с заданием смешанных краевых условий на границе расчетной области. Использованы сопряжённые фундаментальные решения уравнения Лапласа и процедура блуждания по сферам, учитывающая особенности построения траектории движения в окрестности части границы, на которой задается нормальная производная. Предложена процедура совместной реализации двух бессеточных методов фундаментальных решений и Монте-Карло, обеспечивающая повышение точности расчетов. Выполнена верификация комбинированного метода с использованием бенчмарков, в качестве которых выступают результаты, полученные с использованием эталонного решения в квадрате и решения, полученного методом конечных элементов с использованием программного пакета FEMM 4.2, при анализе поля в окрестности зазора электромагнита.

Large eddy simulation of natural convection heat transfer and fluid flow around a horizontal cylinder

Natural convection around a single horizontal cylinder has been extensively studied for heat transfer characteristics, but when coupled with fluid flow, the laminar-to-turbulent transition in buoyant plume poses severe challenge on modelling fidelity and physical interpretability. To address this challenge, this paper conducts detailed verification, validation and analysis of high-fidelity large eddy simulation (LES) for an unconfined horizontal cylinder in water with a Rayleigh number of 8 × 107, complemented by Reynolds-Averaged Navier-Stokes (RANS) computations. To the best of the authors' knowledge, this is the first LES study with acceptable accuracy as validate by experimental data for buoyant plume above a single horizontal cylinder. It is found that LES is far more sensitive to mesh resolution and boundary condition setting than RANS. An alarm is set for the use of periodic condition in LES on lateral boundaries of computational domain due to its inferior accuracy than RANS with transition SST model. The finely-tuned LES with pressure condition on lateral boundaries shows satisfactory agreement with experimental data in terms of heat transfer on cylinder surface and buoyant plume velocity, based on which new physical insight on transitional behavior of thermal plume is obtained. It is found that after leaving the cylinder, buoyant plume is laminar and accelerates, subject to work input from buoyancy force, while its temperature keep decreasing due to heat loss to atmosphere. Flow instability appears first in upward velocity at a streamwise Grashof number of 1.5 × 108, where transition to turbulence onsets. Thermal plume continues to accelerate until it begins to sway horizontally, where energy dissipation into turbulence becomes the major loss mechanism of mean flow energy. Thus, cross-stream diffusivity is augmented notably due to turbulent stresses, leading to smoothing of transverse velocity distribution and reduction of transversely-averaged mean kinetic energy. Transversely-averaged turbulent kinetic energy keeps increasing in transitional regime until the streamwise Grashof number reaches 7 × 109 and then declines to approach an asymptotic value, signifying the end of transition. Overall speaking, buoyancy work dominates the change in mean flow energy, while mean shear outweighs buoyancy in producing turbulent kinetic energy.

Numerical simulation on the whole process of an underwater explosion between a deformable seabed and a free surface

When a charge explodes in shallow water, the combined effects of free surface and seabed on shockwave propagation and bubble motion are significant. In this paper, an underwater explosion between a deformable seabed and a free surface is numerically investigated. An axisymmetric numerical model is established using the Eulerian Finite Element Method (EFEM) and the Volume of Fluid (VOF) method is used in dealing with the interface. The truncated computational domain boundary adopts the non-reflecting boundary condition. The seabed is regarded as a heavier fluid and density ratio between the seabed and water is used to describe seabed feature in this paper. The present model is validated by comparing with the experiment and shows great results. Then the underwater explosion with different initial conditions are simulated, it is found that deformable seabed has a great impact on bubble when the bubble is near the deformable seabed. And the bubble period and pressure peak of shockwave have a positive relation with the density ratio and initial charge depth. In addition, the annular jet might appear and penetrate the upper surface of the bubble in certain condition, leading to the bubble split during the contraction phase.

Numerical investigation of porosity effect on a PCM's thermal performance in a porous rectangular channel via thermal lattice Boltzmann method

This paper performs a numerical assessment of the porosity effect on heat transfer under forced convection in an open-ended horizontal channel filled with a porous structure and a phase change material (PCM). To take into account forced convection between the solid matrix and the PCM, the dimensionless Darcy-Brinkman-Forchheimer equations and the local thermal non-equilibrium condition are considered. Simulations are achieved via the single relaxation time thermal lattice Boltzmann method using three distribution functions to handle the fluid velocity, and fluid and solid temperatures while translating the computational domain boundary conditions in terms of microscopic distribution functions. The numerical outcomes obtained were used to investigate the porosity effect (0.5 ≤ ε ≤ 0.9) on dynamic and thermal fields, entropy generation rate (Ns), and Bejan number (Be) of the considered system under influence of the Reynolds number (Re) during the charging and discharging processes. Based on the findings presented, it can be deduced that, among the various characteristics of metal foam such as conductivity and porosity, the decrease of the latter and the increase in Re speeds up the melting under the unsteady, forced and laminar convection. In addition, the overall irreversibility distribution in the proposed system is dominated by the heat transfer irreversibility.

Semianalytical piezoelastic solution of orthotropic circular cylindrical panel using SBFEM: Bending and free vibrations

A high-performance semi-analytical formulation based on the three-dimensional piezoelectricity theory for bending response and free vibration analysis of circular cylindrical piezoelectric panel subjected to the mechanical and electrical loads is presented. To ensure the accuracy and reliability for the proposed method, a normalized formulation is applied for the constitutive equation of the circular cylindrical piezoelectric panel. By using the scaled boundary finite element method (SBFEM), the normalized dynamic equilibrium equation of cylindrical piezoelectric panel structures in the absence of body force and electric charge is derived into a second-order ordinary differential equation with the analytical form through the weighted residual technique. Under the formulation of the SBFEM, meshes only employed to the boundary of computational domain lead to a reduction of the spatial dimensions by one, so that computation costs can be significantly cut down. After then, the dynamic stiffness equation of whole system is obtained by introducing an intermediate variable. For the static responses, in order to accurately describe the bending behaviors involving the generalized strains and stresses through the thickness, a quadratic function is performed to approximate the generalized displacement vector in the radial direction. For the analysis of free vibrations, the governing equation of motion is rewritten in the expanded form and a condensation of the electric potential degree of freedom is conducted in the system. In this way, the free vibration response of the circular cylindrical piezoelectric panel can be determined by solving the associated eigenvalue problem. Studies of validation and convergence are presented by comparing with those of the published work in which both static and free vibration tests are taken into consideration, and the results show good and convergent performances. Finally, effects of geometric parameters as well as loading conditions on the response characteristics of system are discussed in detail.

A stable dissipative compact finite difference scheme with global accuracy of ninth order

We consider in this paper a ninth-order dissipative compact finite difference scheme. To stabilize the scheme for initial boundary value problems, we introduce the so-called conservative solution points (Deng and Chen, 2018) [9] near the boundaries of computational domain, such that the scheme is stable with global accuracy of ninth order. Various aspects of the scheme are discussed, including the resolution property with respect to the free dissipative parameter appearing in the scheme, the strict stability property for one-dimensional scalar linear advection equations and the issue at the stage of grid generation. Some two-dimensional problems on curvilinear grids are computed to show validity of the scheme.

Performance and stability of the double absorbing boundary method for acoustic-wave propagation

The double absorbing boundary (DAB) is a novel extension to the family of high-order absorbing boundary condition operators. It uses auxiliary variables in a boundary layer to set up cancellation waves that suppress wavefield energy at the computational-domain boundary. In contrast to the perfectly matched layer (PML), the DAB makes no assumptions about the incoming wavefield and can be implemented with a boundary layer as thin as three computational grid-point cells. Our implementation incorporates the DAB into the boundary cell layer of high-order finite-difference (FD) techniques, thus avoiding the need to specify a padding region within the computational domain. We tested the DAB by propagating acoustic waves through homogeneous and heterogeneous 3D earth models. Measurements of the spectral response of energy reflected from the DAB indicate that it reflects approximately 10–15 dB less energy for heterogeneous models than a convolutional PML of the same computational memory complexity. The same measurements also indicate that a DAB boundary layer implemented with second-order FD operators couples well with higher-order FD operators in the computational domain. Long-term stability tests find that the DAB and CPML methods are stable for the acoustic-wave equation. The DAB has promise as a robust and memory-efficient absorbing boundary for 3D seismic imaging and inversion applications as well as other wave-equation applications in applied physics.

The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows

We propose a new computational approach for embedded boundary simulations of hyperbolic systems and, in particular, the linear wave equations and the nonlinear shallow water equations. The proposed approach belongs to the class of surrogate/approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary. Accordingly, boundary conditions, enforced weakly, are appropriately modified to preserve optimal error convergence rates. This framework is applied here in the setting of a stabilized finite element method, even though other spatial discretization techniques could have been employed. Accuracy, stability and robustness of the proposed method are tested by means of an extensive set of computational experiments for the acoustic wave propagation equations and shallow water equations. Comparisons with standard weak boundary conditions imposed on body-fitted grids, which conform to the geometry of the computational domain boundaries, are also presented.

Suppression mechanism study of attached apex drogue on undesirable inflation phenomena

At present, the studies of suppression effect of attached apex drogue on undesirable inflation were seriously dependent on experiments. The experiments were difficult to reveal the suppression mechanism due to the difficulty of data collection. In this paper, a FSI (Fluid Structure Interaction) model based on explicit finite element method was proposed to study the suppression mechanism. The graphical deformation method was used to realize the movement of computational domain. At the same time, the velocity conditions were applied on the boundaries of computational domain, which was used to simulate the external wind field. The coupling between the fluid and structure described by Lagrangian meshes was realized by contact algorithm. Finally, an extra-large parachute was taken as the research object, and the suppression mechanism of attached apex drogue was analyzed according to the numerical results. The effect of different attached apex drogues with different resistance characteristics also was analyzed by the above FSI model. The analysis model and method proposed in this paper could provide the design basis of extra-large parachute.

The wind field in a cattle feedlot: measurements and simulations

Cup and sonic anemometers were operated in and about an empty pen (60 m × 68 m) on the outer (south) edge of a large cattle feedlot in southern Alberta. Mean wind speed, measured at constant height above ground, varied by more than a factor of four across the pen, the spatial transects being distinct for different wind directions—implying (for instance) that efforts to quantify feedlot gas emissions by micrometeorological methods will be prone to error, unless the drastic lateral inhomogeneity of wind statistics is accounted for. A subset of the observations, selected for southerly winds and weak thermal stratification, were aggregated and compared with steady-state, three-dimensional numerical simulations using “ASL3D”, a Reynolds-averaged Navier–Stokes model with eddy viscosity closure that represents the influences both of feedlot windbreak fences and of topography (Wilson, 2018). Simulations confirm that wind drag on the tall (H ≈ 3 m), low porosity (25%) slatted wooden fences was by far the dominant aerodynamic disturbance at this site. Various options were tested for the placement of computational domain boundaries, and it was found that the influence of fences at the faraway edges of neighbouring pens is practically negligible in comparison with that of the fences lying immediately upwind—that is, the transect of relative mean wind speed within the instrumented pen was largely determined by the nearest upwind fence(s). It is also concluded that when the mean wind is obliquely incident on low porosity fences of this type, simulations are improved if the horizontal wind component tangential to the fence is forced to vanish (at the fence).

A comparative study of intake and exhaust port modeling strategies for scale-resolving engine simulations

Due to their capability to capture cycle-to-cycle variations and sporadically occurring phenomena such as misfire and knock, scale-resolving simulations are becoming more and more important for internal combustion engine simulations. Compared to the frequently used unsteady Reynolds-averaged Navier-Stokes approaches, scale-resolving simulations require significantly greater computational costs due to their high spatial and temporal resolution as well as the need to compute several cycles to obtain sufficient statistics. It is well established that the appropriate treatment of boundary conditions is crucial in scale-resolving simulations and both temporally and spatially resolved fluctuations must be prescribed. However, different port modeling strategies can be found in the literature, especially with respect to the extent of the computational domain (boundary close to the flange vs. the entire system up to the plenum) and the numerical treatment of the intake/exhaust when the valves are closed (enabled vs. disabled). This study compares three different port modeling strategies, namely a long ports version, a short ports version and a version with short and temporarily disabled ports based on the well-established Darmstadt benchmark engine. The aim is to identify the requirements for scale-resolving simulations in terms of the treatment of the intake and the exhaust ports to obtain accurate statistics (mean and variance) and cycle-to-cycle variations of the in-cylinder flow field.

О построении двумерных локально-модифицированных квазиструктурированных сеток и решении на них краевых задач в областях с криволинейной границей последовательных наблюдений

New approaches to local modification quasistructured grids, which allow to track the inhomogeneous boundary value problems in the computational domain and adaptable to curved boundaries, as well as easy to use and does not require the storage of large amounts of data as required in unstructured grids are developed. Such grids are proposed to use for the efficient simulation of a wide class of electro physical devices. It is experimentally shown the need for a local modification of the rectangular grid in calculations in domains with curvilinear boundary. The two-step algorithms for local modifications of considered quasistructured grids are developed. On the first step modification of the near boundary nodes is carried out by the its shift along the normal to boundary and on the second step the transformation of the grid elements that do not meet the quality criteria in a quality grid elements is carried out. Special algorithms for such transformations, which do not violate the structuring subgrids in subdomains are developed. Recommendations for the construction of grids on the interface of subdomains that contain the uncoordinated grids have been done. Algorithms local modification of grids on the interface between the subdomains, one of which contains a segment of the computational domain boundaries, have been developed. The series of numerical experiments on solving a model problem are carried out. The results of numerical experiments showed the validity of the proposed approaches.

Effect of domain boundary set on natural convection heat transfer characteristics for vertical annular finned tube heat exchanger

The main purpose of this study is to use the three-dimensional commercial package along with experimental data and the inverse result of the heat transfer coefficient to investigate the effect of the computational domain boundary set on the natural convection heat transfer and fluid flow characteristics of single-tube vertical annular fin and tube heat exchanger in a box with an upward opening. Various flow models are introduced. The air temperature and velocity profiles, fin temperature and heat transfer coefficient on the fins are determined by the commercial package. More accurate numerical results and an appropriate flow model can be obtained if the resulting heat transfer coefficient and the fin temperature are close to the inverse result and experimental fin temperature data, respectively. However, differences in boundary condition set at the side walls of the box can affect air velocity and temperature profiles. The choice of the appropriate flow model can also be related to the boundary set of the computational domain. Thus, the suitability of the boundary condition set must be checked at the side walls of the box.

Assessment of single-sided natural ventilation driven by buoyancy forces through variable window configurations

Natural ventilation has great potential to create desirable indoor air quality and reduce energy consumption in buildings. Accurately modeling the windows of buildings is important to quantify airflow in single-sided natural ventilation. However, a simplification of real windows into rectangular openings has been widely applied in published literature, which seriously affects predictions of airflow through real windows. This investigation numerically evaluates the performances of real windows in the case of buoyancy-driven, single-sided ventilation. Several typical windows used in buildings are analyzed. The Reynolds-averaged Navier-Stokes (RANS) model and k-ω turbulence model are combined to solve airflow characteristics inside and outside the building. The results reveal that the computational fluid dynamics (CFD) model is sensitive to computational domain sizes and boundary conditions, while the sensitivities for different window configurations are different. The ventilation rates and thermal profiles inside the building varied for each window type, although the open window areas are almost identical. According to the comparison of CFD and analytical methods, it was found that the specification of constant discharge coefficients is no longer suitable to estimate the ventilation rates through real windows, and further investigations are needed to find better estimates of the coefficients for a particular window configuration.

DgSMC-B code: A robust and autonomous direct simulation Monte Carlo code for arbitrary geometries

In this paper, we describe the structure of a new Direct Simulation Monte Carlo (DSMC) code that takes advantage of combinatorial geometry (CG) to simulate any rarefied gas flows Medias. The developed code, called DgSMC-B, has been written in FORTRAN90 language with capability of parallel processing using OpenMP framework. The DgSMC-B is capable of handling 3-dimensional (3D) geometries, which is created with first-and second-order surfaces. It performs independent particle tracking for the complex geometry without the intervention of mesh. In addition, it resolves the computational domain boundary and volume computing in border grids using hexahedral mesh. The developed code is robust and self-governing code, which does not use any separate code such as mesh generators. The results of six test cases have been presented to indicate its ability to deal with wide range of benchmark problems with sophisticated geometries such as airfoil NACA 0012. The DgSMC-B code demonstrates its performance and accuracy in a variety of problems. The results are found to be in good agreement with references and experimental data.