Domain Boundary Conditions Research Articles

Fast Computation of Domain Boundary Conditions Using Splines in Penalized VIC Method

In the vortex-in-cell method combined with the penalization method, fluid particles are traced by continuously updating their positions and strengths from the grid solution. To evaluate particle velocity, the velocity field is computed by solving a Poisson equation for the vector potential, namely [Formula: see text], where [Formula: see text], and its computation can be greatly accelerated by the use of a fast Poisson solver. While this method offers an efficient way to simulate unsteady viscous flows, the computation of the boundary values when solving the Poisson equation can become a computation time bottleneck. Although adopting the fast multipole method can lead to saving further computation time, its disadvantage is that it requires complicated hierarchical data structures such as a quad-tree and oct-tree. In this paper, we introduce and assess an approximation method for specifying domain boundary values using splines. Using the proposed spline approximation method we achieve significant savings in both computation time and memory consumption.

Energy decay for the wave equation of variable coefficients with acoustic boundary conditions in domains with nonlocally reacting boundary

In this paper, we consider the wave equation of variable coefficients with acoustic boundary conditions in domains with nonlocally reacting boundary. This work is devoted to prove the energy decay for the wave equation of variable coefficients having some boundary reacting conditions. This paper is to improve our previous result in Ha (2016) by applying the variable coefficients case.

A fast immersed interface method for the Cahn–Hilliard equation with arbitrary boundary conditions in complex domains

A fast immersed boundary method for the Cahn–Hilliard equation is introduced. The decomposition of the fourth-order non-linear Cahn–Hilliard equation into a system of linear parabolic second-order equations allows to pose arbitrary Neumann or surface wetting conditions on the boundary. In space a finite-volume discretization on a regular Cartesian voxel grid allows the use of fast parabolic solvers via Fourier transform of arbitrary convergence order. For the time discretization, a second-order Runge–Kutta scheme is applied. The polynomial approximation of the chemical potential results in a numerical scheme that is unconditionally gradient-stable and allows large time steps. With an additional pre-conditioner for the linear system, the condition of linear system is minimized. By this the convergence is independent of both spatial discretization and time step size. This allows for the simulation of phase separation in large porous complex domains with three dimensions and over hundred million degrees of freedom while applying arbitrary boundary conditions and using large time steps.

A novel method for the solution of Blasius equation in semi-infinite domains

Many known methods fail in the attempt to get analytic solutions of Blasius-type equations. In this work, we apply the reproducing kernel method for ivestigating Blasius equations with two different boundary conditions in semi-infinite domains. Convergence analysis of the reproducing kernel method is given. The numerical approximations are presented and compared with some other techniques, Howarth's numerical solution and Runge-Kutta Fehlberg method.

Gradient estimates of mean curvature equation with Neumann boundary condition in domains of Riemannian manifold

We study the prescribed mean curvature equation with Neumann boundary conditions in domains of Riemannian manifold. The main goal is to establish the gradient estimates for solutions by the maximum principle. As a consequence, we obtain an existence result.

The Boltzmann Equation with Specular Boundary Condition in Convex Domains

We establish the global well‐posedness and stability of the Boltzmann equation with the specular reflection boundary condition in general smooth convex domains when an initial datum is close to the Maxwellian with or without a small external potential. In particular, we have completely solved the longstanding open problem after an announcement by Shizuta and Asano in 1977. © 2017 Wiley Periodicals, Inc.

A GPU‐accelerated nodal discontinuous Galerkin method with high‐order absorbing boundary conditions and corner/edge compatibility

SummaryDiscontinuous Galerkin finite element schemes exhibit attractive features for accurate large‐scale wave‐propagation simulations on modern parallel architectures. For many applications, these schemes must be coupled with nonreflective boundary treatments to limit the size of the computational domain without losing accuracy or computational efficiency, which remains a challenging task. In this paper, we present a combination of a nodal discontinuous Galerkin method with high‐order absorbing boundary conditions for cuboidal computational domains. Compatibility conditions are derived for high‐order absorbing boundary conditions intersecting at the edges and the corners of a cuboidal domain. We propose a GPU implementation of the computational procedure, which results in a multidimensional solver with equations to be solved on 0D, 1D, 2D, and 3D spatial regions. Numerical results demonstrate both the accuracy and the computational efficiency of our approach.

Well-conditioned boundary integral equation formulations and Nyström discretizations for the solution of Helmholtz problems with impedance boundary conditions in two-dimensional Lipschitz domains

We present a regularization strategy that leads to well-conditioned boundary integral equation formulations of Helm\-holtz equations with impedance boundary conditions in two-dimensional Lipschitz domains. We consider both the case of classical impedance boundary conditions, as well as that of transmission impedance conditions wherein the impedances are certain coercive operators. The latter type of problem is instrumental in the speed up of the convergence of Domain Decomposition Methods for Helmholtz problems. Our regularized formulations use as unknowns the Dirichlet traces of the solution on the boundary of the domain. Taking advantage of the increased regularity of the unknowns in our formulations, we show through a variety of numerical results that a graded-mesh based Nystr\om discretization of these regularized formulations leads to efficient and accurate solutions of interior and exterior Helmholtz problems with impedance boundary conditions.

Homogenization in perforated domains and interior Lipschitz estimates

We establish interior Lipschitz estimates at the macroscopic scale for solutions to systems of linear elasticity with rapidly oscillating periodic coefficients and mixed boundary conditions in domains periodically perforated at a microscopic scale ε by establishing H1-convergence rates for such solutions. The interior estimates are derived directly without the use of compactness via an argument presented in [3] that was adapted for elliptic equations in [2] and [11]. As a consequence, we derive a Liouville type estimate for solutions to the systems of linear elasticity in unbounded periodically perforated domains.

Optimum configuration for accurate simulations of chaotic porous media with Lattice Boltzmann Methods considering boundary conditions, lattice spacing and domain size

Simulations of the flow field through chaotic porous media are powerful numerical challenges of special interest in science and technology. The simulations are usually done over representative samples which summarise the properties of the material. Several factors affect the accuracy of the results. Firstly the spatial resolution has to be fine enough to be able to capture the smallest geometrical details. Secondly the domain size has to be large enough to contain the large characteristic scale of the porous media. And finally the effects induced by the boundary conditions have to be diluted when more realistic options are not available. This is the case when the geometry is obtained by tomography and the periodic boundary conditions cannot be applied to delimit the sample because its geometry is not periodic. Impermeable boundary conditions are usually chosen to enclose the domain, forcing mass conservation. As a result, the flow field is over-restricted and the total pressure drop can be over-estimated. In this paper a new strategy is presented to optimise the computational resources consumption keeping the restrictions imposed by the accuracy criteria. The effects of the domain size, discretisation thickness and boundary condition disturbances are studied in detail. The study starts with the procedural generation of chaotic porous walls which mimics acicular mullite filters. An advantage of this process is the possibility to create periodic geometries. Periodicity permits the application of advanced techniques such as cyclic cross-correlations between the phase field and the velocity component fields without aliasing. From cross-correlation operations the large characteristic scale is obtained. The result is a lower threshold for the domain size. In second place a mesh independent study is done to find the upper threshold for the lattice spacing. The Minkowski–Bouligand fractal dimension of the fluid–solid interface corroborates the results. It has been demonstrated how the fractal dimension is a good candidate to replace the mesh independent study with lower computational cost for this type of problems. The last step is to compare the results obtained for a periodic geometry applying periodicity and symmetry as boundary conditions. Considering the periodic case as reference the resultant error is analysed. The explanation of the analysis includes how the intensity of the error changes in space and the limitations of symmetric boundary conditions.

Flame resolved simulation of a turbulent premixed bluff-body burner experiment. Part II: A-priori and a-posteriori investigation of sub-grid scale wrinkling closures in the context of artificially thickened flame modeling

Dynamic sub-filter closures for artificially thickened flame (ATF) combustion models for large eddy simulation (LES) are investigated with consistent a-priori and a-posteriori analyses. The analyses are based on a flame resolved simulation (quasi DNS) and large eddy simulations of the bluff body burner experiment by Hochgreb and Barlow with premixed flamelet generated manifolds (PFGM). Both flame resolved simulation and LES are performed under the conditions of a single real flame experiment, using the same domain size, filter sizes, boundary conditions and numerics, all with an additional validation by comparison to experimental data. For the evaluation of the sub-filter wrinkling factor, the well-established model by Charlette et al. (2002) in the modified version by Wang et al. (2011) is used with a static and with a dynamic model parameter, a new dynamic power-law model is discussed additionally. In the a-priori analysis, the probability density functions (PDFs) of the sub-grid scale (SGS) wrinkling factor are compared against the modeled ones based on the flame resolved simulation data. These a-priori modeled wrinkling factor PDFs are then compared against the a-posteriori ones from the LES results, where a similar shape is observed for all models. The static model tends to over-predict the wrinkling factor, a better agreement is found for the dynamic models for the medium and small filter width, where the new formulation improves the results for the latter. For the largest filter width, the wrinkling factor is under-predicted by the dynamic models. This under-prediction is, however, compensated by larger gradients of the progress variable field so that the mean flame surface density conditioned on the progress variable is in closer agreement with the flame resolved simulation than the wrinkling factor PDFs are. Finally, radial profiles of the time-averaged temperature from the LES, flame resolved simulation and experiment are compared against each other. With the dynamic SGS wrinkling models, the LES results converge with grid refinement against the flame resolved simulation results.

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.

A local artificial boundary for transient seepage problems with unsteady boundary conditions in unbounded domains

AbstractNumerical analysis of transient seepage in unbounded domains with unsteady boundary conditions requires a more sophisticated artificial boundary approach to deal with the infinite character of the domain. To that end, a local artificial boundary is established by simplifying a global artificial boundary. The global artificial boundary conditions (ABCs) at the truncated boundary are derived from analytical solutions for one‐dimensional axisymmetric diffusion problems. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global ABCs are simplified to local ABCs to significantly enhance the computational efficiency. The proposed local ABCs are implemented in a finite element computer program so that the solutions to various seepage problems can be calculated. The proposed approach is first verified by the computation of a one‐dimensional radial flow problem and then tentatively applied to more general two‐dimensional cylindrical problems and planar problems. The solutions obtained using the local ABCs are compared with those obtained using a large element mesh and using a previously proposed local boundary. This comparison demonstrates the satisfactory performance and obvious superiority of the newly established boundary to the other local boundary. Copyright © 2017 John Wiley & Sons, Ltd.

Sensitivity model study of regional mercury dispersion in the atmosphere

Abstract. Atmospheric deposition is the most important pathway by which Hg reaches marine ecosystems, where it can be methylated and enter the base of food chain. The deposition, transport and chemical interactions of atmospheric Hg have been simulated over Europe for the year 2013 in the framework of the Global Mercury Observation System (GMOS) project, performing 14 different model sensitivity tests using two high-resolution three-dimensional chemical transport models (CTMs), varying the anthropogenic emission datasets, atmospheric Br input fields, Hg oxidation schemes and modelling domain boundary condition input. Sensitivity simulation results were compared with observations from 28 monitoring sites in Europe to assess model performance and particularly to analyse the influence of anthropogenic emission speciation and the Hg0(g) atmospheric oxidation mechanism. The contribution of anthropogenic Hg emissions, their speciation and vertical distribution are crucial to the simulated concentration and deposition fields, as is also the choice of Hg0(g) oxidation pathway. The areas most sensitive to changes in Hg emission speciation and the emission vertical distribution are those near major sources, but also the Aegean and the Black seas, the English Channel, the Skagerrak Strait and the northern German coast. Considerable influence was found also evident over the Mediterranean, the North Sea and Baltic Sea and some influence is seen over continental Europe, while this difference is least over the north-western part of the modelling domain, which includes the Norwegian Sea and Iceland. The Br oxidation pathway produces more HgII(g) in the lower model levels, but overall wet deposition is lower in comparison to the simulations which employ an O3 ∕ OH oxidation mechanism. The necessity to perform continuous measurements of speciated Hg and to investigate the local impacts of Hg emissions and deposition, as well as interactions dependent on land use and vegetation, forests, peat bogs, etc., is highlighted in this study.

Broadband liner impedance eduction for multimodal acoustic propagation in the presence of a mean flow

A new broadband impedance eduction method is introduced to identify the surface impedance of acoustic liners from in situ measurements on a test rig. Multimodal acoustic propagation is taken into account in order to reproduce realistic conditions. The present approach is based on the resolution of the linearized 3D Euler equations in the time domain. The broadband impedance time domain boundary condition is prescribed from a multipole impedance model, and is formulated as a differential form well-suited for high-order numerical methods. Numerical values of the model coefficients are determined by minimizing the difference between measured and simulated acoustic quantities, namely the insertion loss and wall pressure fluctuations at a few locations inside the duct. The minimization is performed through a multi-objective optimization thanks to the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The present eduction method is validated with benchmark data provided by NASA for plane wave propagation, and by synthesized numerical data for multimodal propagation.

Numerical analysis of eccentric orifice plate using ANSYS Fluent software

In this paper the eccentric orifice plate is qualitative analysed as compared with the classical concentric orifice plate from the point of view of sedimentation tendency of solid particles in the fluid whose flow rate is measured. For this purpose, the numerical streamlines pattern will be compared for both orifice plates. The numerical analysis has been performed using ANSYS Fluent software. The methodology of CFD analysis is presented: creating the 3D solid model, fluid domain extraction, meshing, boundary condition, turbulence model, solving algorithm, convergence criterion, results and validation. Analysing the numerical streamlines, for the concentric orifice plate can be clearly observed two circumferential regions of separated flows, upstream and downstream of the orifice plate. The bottom part of these regions are the place where the solid particles could sediment. On the other hand, for the eccentric orifice plate, the streamlines pattern suggest that no sedimentation will occur because at the bottom area of the pipe there are no separated flows.

Atom-partitioned multipole expansions for electrostatic potential boundary conditions

Applications such as grid-based real-space density functional theory (DFT) use the Poisson equation to compute electrostatics. However, the expected long tail of the electrostatic potential requires either the use of a large and costly outer domain or Dirichlet boundary conditions estimated via multipole expansion. We find that the oft-used single-center spherical multipole expansion is only appropriate for isotropic mesh domains such as spheres and cubes. In this work, we introduce a method suitable for high aspect ratio meshes whereby the charge density is partitioned into atomic domains and multipoles are computed for each domain. While this approach is moderately more expensive than a single-center expansion, it is numerically stable and still a small fraction of the overall cost of a DFT calculation. The net result is that when high aspect ratio systems are being studied, form-fitted meshes can now be used in lieu of cubic meshes to gain computational speedup.

Numerical Simulation of time domain wall impedance on circular and annular ducts using the immersed boundary method

In this work, time domain boundary conditions of wall impedance are simulated on circular and annular ducts of constant cross section. The discretization technique used here is the immersed boundary method in the framework of finite volume formulation. It has fourth order of precision in space and uses a third order Runge-Kutta method for time stepping. Several boundary conditions for wall impedance are tested and then compared with the analytical results of the one-dimensional resonating chamber for code validation. The impedance boundary conditions are simulated on a circular duct with wall treatment and with a synthetic sound source. Mean flow conditions include constant axial velocity and swirling flows of rigid body rotation and potential flow. The results are then compared with a fourth order eigensystem method of linearized governing equations. The results of the immersed boundary methodology are assessed along with the wall impedance boundary condition models and their linear validity is compared with the results of the eigensystem method.

Nonsymmetric elliptic operators with Wentzell boundary conditions in general domains

We study nonsymmetric second order elliptic operators with Wentzell boundary conditions in general domains with sufficiently smooth boundary. The ambient space is a space of $L^p$- type, $1\le p\le \infty$. We prove the existence of analytic quasicontractive $(C_0)$-semigroups generated by the closures of such operators, for any $1< p< \infty$. Moreover, we extend a previous result concerning the continuous dependence of these semigroups on the coefficients of the boundary condition. We also specify precisely the domains of the generators explicitly in the case of bounded domains and $1 < p < \infty$, when all the ingredients of the problem, including the boundary of the domain, the coefficients, and the initial condition, are of class $C^{\infty}$.

Multi-component Cahn–Hilliard system with different boundary conditions in complex domains

We propose an efficient phase-field model for multi-component Cahn–Hilliard (CH) systems in complex domains. The original multi-component Cahn–Hilliard system with a fixed phase is modified in order to make it suitable for complex domains in the Cartesian grid, along with contact angle or no mass flow boundary conditions on the complex boundaries. The proposed method uses a practically unconditionally gradient stable nonlinear splitting numerical scheme. Further, a nonlinear full approximation storage multigrid algorithm is used for solving semi-implicit formulations of the multi-component CH system, incorporated with an adaptive mesh refinement technique. The robustness of the proposed method is validated through various numerical simulations including multi-phase separations via spinodal decomposition, equilibrium contact angle problems, and multi-phase flows with a background velocity field in complex domains.