Stabilized finite element methods to predict ventilation efficiency and thermal comfort in buildings

Lube, Gert; Knopp, Tobias; Rapin, Gerd; Gritzki, Ralf; Rösler, Markus

doi:10.1002/fld.1790

Cited by 15 publications

(10 citation statements)

References 29 publications

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“…The devising of suitable numerical methods for solving the Boussinesq equations and its generalizations, such as temperature‐dependent coefficient problems, has become a very active research area in recent years (see, e.g., Refs. , and the references therein). This fact has been motivated by its diverse applications in industry (fume cupboard ventilation, heat exchangers, cooling of electronic equipments, cooling of nuclear reactors, etc.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, we derive optimal a priori error estimates, and provide several numerical results illustrating the good performance of the augmented mixed-primal finite element method and confirming the theoretical rates of convergence.The devising of suitable numerical methods for solving the Boussinesq equations and its generalizations, such as temperature-dependent coefficient problems, has become a very active research area in recent years (see, e.g., Refs. [1][2][3][4][5][6][7][8], and the references therein). This fact has been motivated by its diverse applications in industry (fume cupboard ventilation, heat exchangers, cooling of electronic equipments, cooling of nuclear reactors, etc.…”

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confidence: 99%

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Analysis of an augmented mixed‐primal formulation for the stationary Boussinesq problem

Colmenares

Gatica

Oyarzúa

2015

Numerical Methods Partial

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In this article, we propose and analyze a new mixed variational formulation for the stationary Boussinesq problem. Our method, which uses a technique previously applied to the Navier-Stokes equations, is based first on the introduction of a modified pseudostress tensor depending nonlinearly on the velocity through the respective convective term. Next, the pressure is eliminated, and an augmented approach for the fluid flow, which incorporates Galerkin-type terms arising from the constitutive and equilibrium equations, and from the Dirichlet boundary condition, is coupled with a primal-mixed scheme for the main equation modeling the temperature. In this way, the only unknowns of the resulting formulation are given by the aforementioned nonlinear pseudostress, the velocity, the temperature, and the normal derivative of the latter on the boundary. An equivalent fixed-point setting is then introduced and the corresponding classical Banach Theorem, combined with the Lax-Milgram Theorem and the Babuška-Brezzi theory, are applied to prove the unique solvability of the continuous problem. In turn, the Brouwer and the Banach fixed-point theorems are used to establish existence and uniqueness of solution, respectively, of the associated Galerkin scheme. In particular, Raviart-Thomas spaces of order k for the pseudostress, continuous piecewise polynomials of degree ≤ k+1 for the velocity and the temperature, and piecewise polynomials of degree ≤ k for the boundary unknown become feasible choices. Finally, we derive optimal a priori error estimates, and provide several numerical results illustrating the good performance of the augmented mixed-primal finite element method and confirming the theoretical rates of convergence.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Analysis of an augmented mixed‐primal formulation for the stationary Boussinesq problem

Colmenares

Gatica

Oyarzúa

2015

Numerical Methods Partial

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“…by solving the integral equation. It is common practice to model the indoor airflow as lowturbulent hydrodynamic flow [27,33] and to solve it with the necessary high resolution in space and time. However, with these new requirements RHT may become the computational bottleneck, a role previously played by convective heat transfer.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of radiative heat transfer in indoor environments on programmable graphics hardware

Kramer

Gritzki

Perschk

et al. 2015

International Journal of Thermal Sciences

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“…Consequently, energy optimization for space cooling maintaining thermal comfort has attracted significant attention recently (see [2,3] and references therein). While the importance of energy consumption is often exacerbated, the indoor air quality (IAQ) is not usually discussed [4]. However, IAQ is an important parameter that determines the productivity and performance of occupants in the building.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Ventilation System and Soft-Sensors for Maintaining Indoor Air Quality and Thermal Comfort in Buildings

et al. 2020

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Maintaining both indoor air quality (IAQ) and thermal comfort in buildings along with optimized energy consumption is a challenging problem. This investigation presents a novel design for hybrid ventilation system enabled by predictive control and soft-sensors to achieve both IAQ and thermal comfort by combining predictive control with demand controlled ventilation (DCV). First, we show that the problem of maintaining IAQ, thermal comfort and optimal energy is a multi-objective optimization problem with competing objectives, and a predictive control approach is required to smartly control the system. This leads to many implementation challenges which are addressed by designing a hybrid ventilation scheme supported by predictive control and soft-sensors. The main idea of the hybrid ventilation system is to achieve thermal comfort by varying the ON/OFF times of the air conditioners to maintain the temperature within user-defined bands using a predictive control and IAQ is maintained using Healthbox 3.0, a DCV device. Furthermore, this study also designs soft-sensors by combining the Internet of Things (IoT)-based sensors with deep-learning tools. The hardware realization of the control and IoT prototype is also discussed. The proposed novel hybrid ventilation system and the soft-sensors are demonstrated in a real research laboratory, i.e., Center for Research in Automatic Control Engineering (C-RACE) located at Kalasalingam University, India. Our results show the perceived benefits of hybrid ventilation, predictive control, and soft-sensors.

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Stabilized finite element methods to predict ventilation efficiency and thermal comfort in buildings

Cited by 15 publications

References 29 publications

Analysis of an augmented mixed‐primal formulation for the stationary Boussinesq problem

Analysis of an augmented mixed‐primal formulation for the stationary Boussinesq problem

Numerical simulation of radiative heat transfer in indoor environments on programmable graphics hardware

Hybrid Ventilation System and Soft-Sensors for Maintaining Indoor Air Quality and Thermal Comfort in Buildings

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