Boundary Conditions For Calculation Research Articles

Sensitivity-Aware Density Estimation in Multiple Dimensions.

We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage of the computational speed and flexible boundary conditions offered by splines on a grid. We choose to regularize the Hessian of the spline via the nuclear norm to promote sparsity. As a result, the method is spatially adaptive and stable against the choice of the regularization parameter, which plays the role of the bandwidth. We test our computational pipeline on standard densities and provide software. We also present a new approach to PET rebinning as an application of our framework.

Computational Lower Limb Simulator Boundary Conditions to Reproduce Measured TKA Loading in a Cohort of Telemetric Implant Patients.

Recent advancements in computational modeling offer opportunities to refine total knee arthroplasty (TKA) design and treatment strategies. This study developed patient-specific simulator external boundary conditions (EBCs) using a PID-controlled lower limb finite element (FE) model. Calibration of the external actuation required to achieve measured patient-specific joint loading and motion was completed for nine patients with telemetric implants during gait, stair descent, and deep knee bend. The study also compared two EBC scenarios: activity-specific hip AP motion and pelvic rotation (that was averaged across all patients for an activity) and patient-specific hip AP motion and pelvic rotation. Including patient-specific data significantly improved reproduction of joint-level loading, reducing root mean squared error between the target and achieved loading by 28.7% and highlighting the importance of detailed patient data in replicating joint kinematics and kinetics. The principal component analysis (PCA) of the EBCs for the patient dataset showed that one component represented 77.8% of the overall variation, while the first three components represented 97.8%. Given the significant loading variability within the patient cohort, this group of patient-specific models can be run individually to provide insight into expected TKA mechanics variability, and the PCA can be utilized to further create reasonable EBCs that expand the variability evaluated.

Turbulence Measurements Downstream of a Combustor Simulator Designed for Studies on the Combustor–Turbine Interaction

Turbulence intensity impacts the performance of turbine stages and it is an important inlet boundary condition for CFD computations; the knowledge of its value at the turbine inlet is then of paramount importance. In combustor–turbine interaction experimental studies, combustor simulators replace real combustors and allow for the introduction of flow perturbation at the turbine inlet. Therefore, the turbulence intensity of a combustor simulator used in a wide experimental campaign at Politecnico di Milano is characterized using a hot-wire probe in a blow-down wind tunnel, and the results are compared to URANS CFD computations. This combustor simulator can generate a combination of a swirl profile with a steady/unsteady temperature disturbance. In the cold unsteady disturbance case, hot-wire measurements are phase-averaged at the frequency of the injected perturbation. The combustor simulator turbulence intensity is measured at two different axial positions to understand its evolution.

Optimizing vehicle aerodynamics through the synergistic application of Design of Experiments (DoE) and Computational Fluid Dynamics (CFD)

The aerodynamic design of cars not only creates aesthetic and diverse car shapes, but also ensures their safety and fuel economy. According to Mustafa Cakir's research[1], approximately of the fuel consumption of a car traveling at high speeds is used to counteract air resistance. However, with the increasing severity of global warming, emissions standards for automobile exhaust are becoming increasingly stringent. Considering that gasoline vehicles still dominate the household car market, optimizing the aerodynamic design of automobiles is imperative. This work analyzes and optimizes the aerodynamic design of automobiles through the synergistic application of Design of Experiments (DoE) and Computational Fluid Dynamics (CFD). Before conducting experiments, the article first introduces and derives the basic control equations of computational fluid dynamics, namely the continuity equation and Navier-Stokes equation, and describes how they are used in experiments. Then, the article briefly introduces the drag coefficients of automobiles, which are important theoretical basis for subsequent aerodynamic design optimization in this article. In the experimental part, this study focuses on the influence of four important design parameters: angle of the front window , angle of the hood , angle of the back window , and length of the trunk . Using Solidworks 3D modeling software, the article simulates these design parameters and prepares for CFD numerical simulation by geometry, setting computational domain, boundary conditions, and objective functions, and generating mesh. Based on the DoE and numerical simulation results, the article ultimately selects a front window angle of , a hood angle of , a back window of , and as the optimized design. Compared with the basic model, the optimized model reduces the drag coefficient by about . The conclusion of this study provides ideas and theoretical basis for the aerodynamic optimization design of new generation automobiles with the incorporation of DoE. However, the design parameters of automobiles are countless, and in the future, this article will strive to research and simulate more diverse automobile designs and analyze their aerodynamic performance to explore more optimized designs.

Realistic turbulent inflow conditions for estimating the performance of a floating wind turbine

Abstract. A novel method for generating turbulent inflow boundary conditions for aeroelastic computations is proposed, based on interfacing hybrid hot-wire and particle image velocimetry measurements performed in a wind tunnel to a full-scale load simulation conducted with FAST. This approach is based on the use of proper orthogonal decomposition (POD) to interpolate and extrapolate the experimental data onto the numerical grid. The temporal dynamics of the temporal POD coefficients is driven by the high-frequency hot-wire measurements used as input for a lower-order model built using a multi-time-delay linear stochastic estimation (LSE) approach. Being directly extracted from the data, the generated three-component velocity fields later used as inlet conditions present correct one- and two-point spatial statistics and realistic temporal dynamics. Wind tunnel measurements are performed at a scale of 1:750, using a properly scaled porous disk as a floating wind turbine model. The motions of the platform are imposed by a linear actuator. Between all 6 degrees of freedom (DOFs) possible, the present study focus on the streamwise direction motion of the model (surge motion). The POD analysis of the flow, with or without considering the presence of the surge motion of the model, shows that a few modes are able to capture the characteristics of the most energetic flow structures and the main features of the wind turbine wake, such as its meandering and the influence of the surge motion. The interfacing method is first tested to estimate the performance of a wind turbine in an offshore boundary layer and then those of a wind turbine immersed in the wake of an upstream wind turbine subjected to a sinusoidal surge motion. Results are also compared to those obtained using the standard inflow generation method provided by TurbSim available in FAST.

Hydrodynamics and sediment transport in Poyang Lake under the effects of wind and backflow

Abstract The ecology of the aquatic environment in Poyang Lake, the largest fresh lake in China, is notably impacted by the backflow from the Yangtze River, which conveys a high flux of sediments. This study employs a widely recognized numerical model to replicate the backflow in 2007 (the strongest backflow after the operation initiation of the Three Gorges Dam) to investigate the contributions of wind and backflow to the sediment transport process. The results show that the influences of wind and backflow on flow patterns and sediment transport processes have significant spatial heterogeneity. In the narrow waterway leading to the central lake area, hydrodynamics is mainly driven by backflow. Conversely, the hydrodynamics of the open expanse of the lake is primarily influenced by wind forces. Dominant wind leads to the formation of gyres, which significantly alter flow paths and push sediment into the upstream areas. As a result, the suspended sediment area expands at an average rate of 20.1–21.3 km2 daily, marking a 75–85% surge compared to the no wind condition (11.5 km2). The study facilitates a deeper understanding of sediment transport processes in large lakes.

Defining the Computational Domain and Boundary Conditions for Fluid Flow in a Mining Excavation

Defining the Computational Domain and Boundary Conditions for Fluid Flow in a Mining Excavation

Flame Surface Density and Artificially Thickened Flame Combustion Models Applied to a Turbulent Partially-Premixed Flame

The Sydney Flame provides an excellent framework for systematic analysis of premixed, partially premixed and non-premixed methane/air combustion. It represents (depending on the axial position from the fuel inlet) non-premixed, partially premixed and fully premixed combustion. We simulate the test case FJ200-5GP-Lr75-57, which represents the partially premixed mode. Large-eddy simulations (LES) are conducted using a flame surface density combustion model (FSD) using one-step chemistry and an artificially thickened flame model (ATF) with a global two-step and an analytically reduced multi-step chemistry reaction mechanism. Unity Lewis numbers are assumed (Le=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Le=1$$\\end{document}) at first. The FSD and ATF models are compared using the same computational mesh, numerical scheme and boundary conditions. Both models will be analysed regarding their accuracy and computational efficiency in the regime of partially premixed combustion. A comparison of the results points out the strengths and weaknesses of the FSD models. The FSD model with inclusion of flame stretch effects yields good agreement with mean experimental temperature, CO2 and H2O mass fraction distributions in contrast to the ATF model using the global two-step mechanism, which overestimates downstream temperature, CO2 and H2O mass fractions. The FSD model performs well in all regions, which are dominated first by premixed, then partially premixed and finally non-premixed combustion along the flame. The ATF multi-step chemistry shows good results only in the premixed mode region, while mean temperature, CO2 and mass fractions are overestimated in the non-premixed mode regions at higher mixture fraction values. Including differential diffusion into the transport equations improved the ATF model results in comparison with experiments. A mesh study revealed, that the ATF model performs only after mesh refinement. In particular results are improved in the non-premixed combustion region. In contrast, the FSD model is less resolution sensitive and performs very well for both meshes. An evaluation of the Wasserstein metric provides a quantitative assessment of different ATF model setups on simulation accuracy. Finally, computational times for all simulation setups are compared.

Numerical simulations of Darcy-forchheimer flow of radiative hybrid nanofluid with Lobatto-IIIa scheme configured by a stretching surface

Heat transport and energy storage continue to be major issues for manufacturers and scientists. So far, the notion of novel heat transfer fluids has been developed, namely nanofluids and hybrid nanofluids. This investigation examines thermal radiation effect on heat transfer in MHD flow using the hybrid nanofluid. It examines a hybrid nanofluid (SWCNT-Al2O3/H2H6O2–H2O and MWCNT-CuO/H2H6O2–H2O) with H2O water base fluid nature passing through a starching surface with thermal radiation, Biot number and melting phenomena. The suitable similarity transformations are used to transmute the main governing system of equation PDEs and the appropriate boundary conditions for computation with the help of well-reputed shooting technique. The graphical and numerical outcomes against dissimilar flow parameters are computed by the mathematical software MATLAB. The velocity distribution profile is decreased by growing values of the Rotation parameter and porosity parameter. The velocity profile is enhanced by increasing the values of Darcy forchheimer medium. The thermal distribution field is enhanced by rising estimations of the thermal radiation parameter and Biot number. Temperature of the fluid is increasing due to increase in thermal conductivity parameter while decreasing due to increase in Marangoni ratio parameter. The present model hybrid nanofluid of heat transmission is evaluated to see if it has higher thermal energy storage efficiency than standard nanofluids. As a result, these novel findings in heat transport might be advantageous in dealing with energy storage issues in the modern technological environment.

Multiple slips and double stratification in MHD flow of hybrid nanofluid past a permeable sheet: triple solutions and stability analysis

Hybrid nanofluid flow past a stretching/shrinking sheet has various applications in industrial and engineering processes, e.g. in glass blowing, the extrusion of polymer sheets, and paper production. Motivated by these numerous uses of hybrid nanofluid in diverse geometries and conditions, the present study analyzes the solutions for MHD flow of Ag-CuO/water hybrid nanofluid past a shrinking sheet. The governing equations and boundary conditions are formulated together with the effects of Brownian motion, double stratification, porous medium, suction, slips, and thermophoresis. Then, similarity transformations are employed to form non-linear ordinary differential equations and boundary conditions for numerical computation in Matlab using the bvp4c solver. A significant finding of triple solutions in the shrinking sheet case prompted a stability analysis to be carried out, and the results show that only the first solution is stable. The effects of controlling parameters on the physical quantities of interest, velocity, temperature, and concentration profiles are analyzed and discussed. The heat and mass transfer rates are noted to improve, with an average of 7.91% and 258.36%, by increasing the Darcy number related to the permeability of the porous medium. Meanwhile, augmenting the nanoparticle volume fraction of Ag from 0.03 to 0.05 enhances the skin friction, heat transfer, and mass transfer rates by 9.4%, 7.36%, and 150.31%, respectively. However, the heat and mass transfer performances of the hybrid nanofluid are inhibited by the double stratification parameters.

Generalized neural closure models with interpretability

Improving the predictive capability and computational cost of dynamical models is often at the heart of augmenting computational physics with machine learning (ML). However, most learning results are limited in interpretability and generalization over different computational grid resolutions, initial and boundary conditions, domain geometries, and physical or problem-specific parameters. In the present study, we simultaneously address all these challenges by developing the novel and versatile methodology of unified neural partial delay differential equations. We augment existing/low-fidelity dynamical models directly in their partial differential equation (PDE) forms with both Markovian and non-Markovian neural network (NN) closure parameterizations. The melding of the existing models with NNs in the continuous spatiotemporal space followed by numerical discretization automatically allows for the desired generalizability. The Markovian term is designed to enable extraction of its analytical form and thus provides interpretability. The non-Markovian terms allow accounting for inherently missing time delays needed to represent the real world. Our flexible modeling framework provides full autonomy for the design of the unknown closure terms such as using any linear-, shallow-, or deep-NN architectures, selecting the span of the input function libraries, and using either or both Markovian and non-Markovian closure terms, all in accord with prior knowledge. We obtain adjoint PDEs in the continuous form, thus enabling direct implementation across differentiable and non-differentiable computational physics codes, different ML frameworks, and treatment of nonuniformly-spaced spatiotemporal training data. We demonstrate the new generalized neural closure models (gnCMs) framework using four sets of experiments based on advecting nonlinear waves, shocks, and ocean acidification models. Our learned gnCMs discover missing physics, find leading numerical error terms, discriminate among candidate functional forms in an interpretable fashion, achieve generalization, and compensate for the lack of complexity in simpler models. Finally, we analyze the computational advantages of our new framework.

Гидродинамика сетных жестких безузловых конструкций

Rigid netting structures are elements, parts of commercial fishing gear and aquaculture cages. They serve to enclose or filter hydrobionts, they are engineering structures. Rigid netting structures can be used as inserts in commercial fishing gear, as well as selective gratings and elements that prevent hydraulic backwater in trawls. They are also elements of stationary fishing gear, such as winders or other fishing gear or barriers. In aquaculture cages, rigid netting structures, the elements of which have a sufficiently large value of the longitudinal and transverse modulus of elasticity E, are parts that ensure the strength of the netting structures. Mesh rigid structures are made of plastic or aluminum rods in the form of cylinders, which can be either smooth or twisted. The article considers the application of a numerical method for determining the hydrodynamic characteristics of mesh rigid structures using the software developed by the authors. A schematization of a rigid netting structure, a mathematical model based on Navier-Stokes partial differential equations, a computational domain, initial and boundary conditions are proposed. The calculation was carried out on a regular computational grid using an implicit finite-difference scheme using the methods of coordinate-wise splitting, linearization of nonlinear equations with subsequent correction of nonlinear coefficients, and solution of the obtained tridiagonal systems by the sweep method. The results of numerical experiments are presented in the form of visualization of pressure on the surface of various mesh structures at various angles of attack.

Nanofluid Flow and Heat Transfer between a Stationary Nonpermeable Disk and a Permeable Rotating Shrinking Disk with Radiation and Heat Generation Effects

The flow between bounded surfaces is known as internal flow. The internal flow between disks has many significant applications, such as gas turbine rotors, rotating machinery, food processing technology, and air cleaning machines. In the current study, the nanofluid flow between two disks, nonpermeable and stationary, and the other permeable, rotating and shrinking, is analysed. The governing partial differential equations and boundary conditions are proposed with the inclusion of radiation and heat generation effects. Then, similarity transformations are utilised in deriving the nonlinear ordinary differential equations and boundary conditions for computation using the bvp4c solver. Multiple solutions are obtained, and only the first solution is stable. The combination Mn-ZnFe2O4/C2H6O2 nanofluid is found to produce the lowest magnitude of skin friction coefficient and the highest heat transfer rate.

On the identification of hypoxic regions in subject-specific cerebral vasculature by combined CFD/MRI.

A long-time exposure to lack of oxygen (hypoxia) in some regions of the cerebrovascular system is believed to be one of the causes of cerebral neurological diseases. In the present study, we show how a combination of magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) can provide a non-invasive alternative for studying blood flow and transport of oxygen within the cerebral vasculature. We perform computer simulations of oxygen mass transfer in the subject-specific geometry of the circle of Willis. The computational domain and boundary conditions are based on four-dimensional (4D)-flow MRI measurements. Two different oxygen mass transfer models are considered: passive (where oxygen is treated as a dilute chemical species in plasma) and active (where oxygen is bonded to haemoglobin) models. We show that neglecting haemoglobin transport results in a significant underestimation of the arterial wall mass transfer of oxygen. We identified the hypoxic regions along the arterial walls by introducing the critical thresholds that are obtained by comparison of the estimated range of Damköhler number (Da ⊂ 〈9; 57〉) with the local Sherwood number. Finally, we recommend additional validations of the combined MRI/CFD approach proposed here for larger groups of subject- or patient-specific brain vasculature systems.

Experimental Methods of Investigating Airborne Indoor Virus-Transmissions Adapted to Several Ventilation Measures.

This study introduces a principle that unifies two experimental methods for evaluating airborne indoor virus-transmissions adapted to several ventilation measures. A first-time comparison of mechanical/natural ventilation and air purification with regard to infection risks is enabled. Effortful computational fluid dynamics demand detailed boundary conditions for accurate calculations of indoor airflows, which are often unknown. Hence, a suitable, simple and generalized experimental set up for identifying the spatial and temporal infection risk for different ventilation measures is more qualified even with unknown boundary conditions. A trace gas method is suitable for mechanical and natural ventilation with outdoor air exchange. For an accurate assessment of air purifiers based on filtration, a surrogate particle method is appropriate. The release of a controlled rate of either trace gas or particles simulates an infectious person releasing virus material. Surrounding substance concentration measurements identify the neighborhood exposure. One key aspect of the study is to prove that the requirement of concordant results of both methods is fulfilled. This is the only way to ensure that the comparison of different ventilation measures described above is reliable. Two examples (a two-person office and a classroom) show how practical both methods are and how the principle is applicable for different types and sizes of rooms.

A computational slip boundary condition for near-wall turbulence modeling

Near-wall turbulence modeling represents one of challengers in the computational fluid dynamics. To tackle this problem, the near-wall non-overlapping domain decomposition (NDD) method proved to be very efficient. It has been successfully used with different Reynolds-averaged Navier–Stokes models. In NDD the computational domain is split into two non-overlapping sub-domains: an inner region near the wall, which is characterized by high gradients, and the outer region. To simplify the solution, in the inner region the thin-layer model can be used. In this case, NDD represents a trade-off between the accuracy and computational time. It has been demonstrated on numerous test cases that NDD is able to save up to one order of computational time while retaining practically high accuracy. A practical drawback of the algorithm is a need to split the computational domain into two regions. In the present paper, for the first time the NDD is realized implicitly. For this purpose, specific boundary conditions of Robin type are derived at the wall. Such boundary conditions reduce the gradients of the solution near the wall. The key property is that the solution can be obtained on a relatively coarse grid and then be recalculated in the inner region. In the approach it is guaranteed that the original outer and updated inner solutions are linked smoothly. The algorithm with the new boundary conditions can be easily implemented in standard codes. This is demonstrated with the code OpenFOAM. In addition, in the paper a more accurate approach to obtain the solution in the inner region is realized. The efficiency of the entire technique is demonstrated on test cases with modeling turbulent flows in a channel and asymmetric diffuser.

An effective LRTC model integrated with total α ‐order variation and boundary adjustment for multichannel visual data inpainting

Restoring damaged multichannel visual data with high loss ratio is quite a challenging task. To address this problem, an effective LRTC (low-rank tensor completion) model integrated with total α-order variation (TVα) in the fractional bounded variation space BVα is proposed to perform superior fractional-in-space regularization. Based on using LR constraint to restore global patterns, TVα regularization is integrated to exploit nonlocally-correlated information on each channel to infer the lost data and simultaneously effectively deal with complex details due to the powerful fractional calculus. Then, a nonlocal fractional regularization strategy for multi-dimensional data and an effective numerical optimization method are creatively designed to solve this problem. Two novel fractional derivative matrix approximations are derived and applied to the first two unfolding modes of the tensor respectively to conveniently solve the fractional regularization subproblem by using an element-wise shrinkage-thresholding operation. In addition, boundary extension and adjustment strategy are designed for the unfolded matrices to alleviate the influence of inaccurate boundary conditions in fractional derivative computations. Experiments are conducted to illustrate its performance and efficiency for YUV video, RGB and HSI restoration, especially its ability to effectively recover complex structures and the details of multi-component visual data with relatively high missing rate.

Locally refined quad meshing for linear elasticity problems based on convolutional neural networks

In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We impose boundary conditions by fixing the position of a part of the boundary and applying a force on another part of the boundary. The resulting displacement and distribution of stresses depend on the geometry of the domain and on the boundary conditions. When applying a standard Galerkin discretization using quadrilateral finite elements, one usually has to perform adaptive refinement to properly resolve maxima of the stress distribution. Such an adaptive scheme requires a local error estimator and a corresponding local refinement strategy. The overall costs of such a strategy are high. We propose to reduce the costs of obtaining a suitable discretization by training a neural network whose evaluation replaces this adaptive refinement procedure. We set up a single network for a large class of possible domains and boundary conditions and not on a single domain of interest. The computational domain and boundary conditions are interpreted as images, which are suitable inputs for convolution neural networks. In our approach we use the U-net architecture and we devise training strategies by dividing the possible inputs into different categories based on their overall geometric complexity. Thus, we compare different training strategies based on varying geometric complexity. One of the advantages of the proposed approach is the interpretation of input and output as images, which do not depend on the underlying discretization scheme. Another is the generalizability and geometric flexibility. The network can be applied to previously unseen geometries, even with different topology and level of detail. Thus, training can easily be extended to other classes of geometries.

On inlet pressure boundary conditions for CT-based computation of fractional flow reserve: clinical measurement of aortic pressure

Background and objectives A quick calculation approach of steady-state fractional flow reserve (FFRss) based on computed tomography angiography (CTA) images is a reliable non-invasive way of calculate FFR, the assumptions used in the research should be study further to increase forecast accuracy. The effect of inlet and outlet boundary conditions on FFRss was investigated. Methods 15 patients who had been diagnosed with coronary artery disease were enrolled in this study. We investigated the sensitivity of calculating FFR to boundary circumstances, using invasive FFR as a benchmark. There are two types of inlet: (1) aortic pressure based on clinically measured. (2) mean pressure calculated based on physiological formula; we further studied the outlet changes of FFRss under different coronary vasodilation responses (24%, 48%, 72%). Results According to the calculate FFR results of all patients, FFRSST (based on the clinical experiment) and FFRSSM (based on the physiological formula) {r = 0.99, [95% confidence interval (CI):0.0.94 to 1.14] (p < 0.001)}. Although the pressure difference between the two pressure boundary conditions is 15 mmHg, the calculated FFR result does not change significantly. The microcirculation resistance of the outlet gradually rose as the vasodilation state changed, and the computed FFR increased. Conclusions A numerical analysis of the effects of proximal and distal boundary constraints of computational models on computed CT-FFR is presented. The findings revealed that distal boundary circumstances (hyperemic vasodilation response of coronary micro-vessels) have a significant impact on FFR, providing evidence to guide the development and application of a computational model for estimating FFR.

Determination of pressure resistance of a partially stoppered vial by using a coupled CFD-0D model of lyophilization

Modeling lyophilization in a vial is frequently done on a single vial level. When setting up a numerical model, the main focus is on heat and mass transfer inside the lyophilizate, whereas the vapor dynamics in the headspace of the vial is taken into account simply through imposing the system pressure as a pressure boundary condition. The present paper offers a deeper insight into the interaction of the sublimated vapor flow and the corresponding vapor pressure conditions inside the headspace of a partially stoppered vial. This is achieved through a coupled numerical solution of the heat and mass transfer inside the product by means of a 0D model describing the frozen domain (ice) and the 3D fluid flow inside the vial geometry with the partially opened stopper, computed by means of Computational Fluid Dynamics. Due to low pressures, the slip flow regime within the continuum hypothesis has to be considered, leading to imposing velocity slip conditions at the solid walls. The 0D model is used for the computation of sublimation mass flow rate as well as heat transfer rate to the vial, with the results of the water vapor mass flow rate and the temperature communicated to the 3D CFD model as a new inlet boundary conditions for computation of compressible fluid flow dynamics inside the vial. The obtained CFD pressure field solution allows derivation of a pressure resistance model for a targeted vial stopper combination, which is then used in calculating the corresponding pressure drop in the headspace of the partially stoppered vial. The coupled CFD-0D model results are validated based on the results of dedicated experimental water runs on several vial and stopper geometries and show, that the vial geometry, but especially the installed stopper, alter the pressure field conditions inside the vial. The increased in-vial local vapor pressure values lead to a decrease of the mass flow rates and an increase of temperatures at the bottom of the product, which range from 0.6 K for the highest system pressure and up to 5.4 K for the lowest system pressure tested. The presented coupled model is suitable for the use in further studies of the impact of various vial forms as well as stoppers on the lyophilization dynamics in a vial.