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1 – 10 of 369Ahmed Berkane and Abdallah Bradji
We consider, as discretization in space, the nonconforming mesh developed in SUSHI (Scheme Using Stabilization and Hybrid Interfaces) developed in Eymard et al. (2010) for a…
Abstract
We consider, as discretization in space, the nonconforming mesh developed in SUSHI (Scheme Using Stabilization and Hybrid Interfaces) developed in Eymard et al. (2010) for a semi-linear heat equation. The time discretization is performed using a uniform mesh. We are concerned with a nonlinear scheme that has been studied in Bradji (2016) in the context of the general framework GDM (Gradient Discretization Method) (Droniou et al., 2018) which includes SUSHI. We provide sufficient conditions on the size of the spatial mesh and the time step which allow to prove a
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This paper presents a Monotonic Unbounded Schemes Transformer (MUST) approach to bound/monotonize (remove undershoots and overshoots) unbounded spatial differencing schemes…
Abstract
Purpose
This paper presents a Monotonic Unbounded Schemes Transformer (MUST) approach to bound/monotonize (remove undershoots and overshoots) unbounded spatial differencing schemes automatically, and naturally. Automatically means the approach (1) captures the critical cell Peclet number when an unbounded scheme starts to produce physically unrealistic solution automatically, and (2) removes the undershoots and overshoots as part of the formulation without requiring human interventions. Naturally implies, all the terms in the discretization equation of the unbounded spatial differencing scheme are retained.
Design/methodology/approach
The authors do not formulate new higher-order scheme. MUST transforms an unbounded higher-order scheme into a bounded higher-order scheme.
Findings
The solutions obtained with MUST are identical to those without MUST when the cell Peclet number is smaller than the critical cell Peclet number. For cell Peclet numbers larger than the critical cell Peclet numbers, MUST sets the nodal values to the limiter value which can be derived for the problem at-hand. The authors propose a way to derive the limiter value. The authors tested MUST on the central differencing scheme, the second-order upwind differencing scheme and the QUICK differencing scheme. In all cases tested, MUST is able to (1) capture the critical cell Peclet numbers; the exact locations when overshoots and undershoots occur, and (2) limit the nodal value to the value of the limiter values. These are achieved by retaining all the discretization terms of the respective differencing schemes naturally and accomplished automatically as part of the discretization process. The authors demonstrated MUST using one-dimensional problems. Results for a two-dimensional convection–diffusion problem are shown in Appendix to show generality of MUST.
Originality/value
The authors present an original approach to convert any unbounded scheme to bounded scheme while retaining all the terms in the original discretization equation.
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Yahya Alnashri and Hasan Alzubaidi
The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary…
Abstract
Purpose
The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary conditions. Then, the authors show that the GDM provides a comprehensive convergence analysis of several numerical methods for the considered model. The convergence is established without non-physical regularity assumptions on the solutions.
Design/methodology/approach
In this paper, the authors use the GDM to discretise a system of reaction diffusion equations with non-homogeneous Dirichlet boundary conditions.
Findings
The authors provide a generic convergence analysis of a system of reaction diffusion equations. The authors introduce a specific example of numerical scheme that fits in the gradient discretisation method. The authors conduct a numerical test to measure the efficiency of the proposed method.
Originality/value
This work provides a unified convergence analysis of several numerical methods for a system of reaction diffusion equations. The generic convergence is proved under the classical assumptions on the solutions.
Details
Keywords
- A gradient discretisation method (GDM)
- Gradient schemes
- Convergence analysis
- Existence of weak solutions
- Two-dimensional reaction–diffusion Brusselator system
- Dirichlet boundary conditions
- Non-conforming finite element methods
- Finite volume schemes
- Hybrid mixed mimetic (HMM) method
- 35K57
- 65N12
- 65M08
Shang-Han Gao and Sheng-Long Nong
This paper aims to analyze the pressure distribution of rectangular aerostatic thrust bearing with a single air supply inlet using the complex potential theory and conformal…
Abstract
Purpose
This paper aims to analyze the pressure distribution of rectangular aerostatic thrust bearing with a single air supply inlet using the complex potential theory and conformal mapping.
Design/methodology/approach
The Möbius transform is used to map the interior of a rectangle onto the interior of a unit circle, from which the pressure distribution and load carrying capacity are obtained. The calculation results are verified by finite difference method.
Findings
The constructed Möbius formula is very effective for the performance characteristics researches for the rectangular thrust bearing with a single air supply inlet. In addition, it is also noted that to obtain the optimized load carrying capacity, the square thrust bearing can be adopted.
Originality/value
The Möbius transform is found suitable to describe the pressure distribution of the rectangular thrust bearing with a single air supply inlet.
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M.S. Daoussa Haggar and M. Mbehou
This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is…
Abstract
Purpose
This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.
Design/methodology/approach
A rigorous error analysis is done, and optimal L2 error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.
Findings
Optimal L2 error estimates and energy norm.
Originality/value
The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.
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Krištof Kovačič, Jurij Gregorc and Božidar Šarler
This study aims to develop an experimentally validated three-dimensional numerical model for predicting different flow patterns produced with a gas dynamic virtual nozzle (GDVN).
Abstract
Purpose
This study aims to develop an experimentally validated three-dimensional numerical model for predicting different flow patterns produced with a gas dynamic virtual nozzle (GDVN).
Design/methodology/approach
The physical model is posed in the mixture formulation and copes with the unsteady, incompressible, isothermal, Newtonian, low turbulent two-phase flow. The computational fluid dynamics numerical solution is based on the half-space finite volume discretisation. The geo-reconstruct volume-of-fluid scheme tracks the interphase boundary between the gas and the liquid. To ensure numerical stability in the transition regime and adequately account for turbulent behaviour, the k-ω shear stress transport turbulence model is used. The model is validated by comparison with the experimental measurements on a vertical, downward-positioned GDVN configuration. Three different combinations of air and water volumetric flow rates have been solved numerically in the range of Reynolds numbers for airflow 1,009–2,596 and water 61–133, respectively, at Weber numbers 1.2–6.2.
Findings
The half-space symmetry allows the numerical reconstruction of the dripping, jetting and indication of the whipping mode. The kinetic energy transfer from the gas to the liquid is analysed, and locations with locally increased gas kinetic energy are observed. The calculated jet shapes reasonably well match the experimentally obtained high-speed camera videos.
Practical implications
The model is used for the virtual studies of new GDVN nozzle designs and optimisation of their operation.
Originality/value
To the best of the authors’ knowledge, the developed model numerically reconstructs all three GDVN flow regimes for the first time.
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Reynolds-averaged Navier–Stokes (RANS) models often perform poorly in shock/turbulence interaction regions, resulting in excessive wall heat load and incorrect representation of…
Abstract
Purpose
Reynolds-averaged Navier–Stokes (RANS) models often perform poorly in shock/turbulence interaction regions, resulting in excessive wall heat load and incorrect representation of the separation length in shockwave/turbulent boundary layer interactions. The authors suggest that this can be traced back to inadequate numerical treatment of the inviscid fluxes. The purpose of this study is an extension to the well-known Harten, Lax, van Leer, Einfeldt (HLLE) Riemann solver to overcome this issue.
Design/methodology/approach
It explicitly takes into account the broadening of waves due to the averaging procedure, which adds numerical dissipation and reduces excessive turbulence production across shocks. The scheme is derived based on the HLLE equations, and it is tested against three numerical experiments.
Findings
Sod’s shock tube case shows that the scheme succeeds in reducing turbulence amplification across shocks. A shock-free turbulent flat plate boundary layer indicates that smooth flow at moderate turbulence intensity is largely unaffected by the scheme. A shock/turbulent boundary layer interaction case with higher turbulence intensity shows that the added numerical dissipation can, however, impair the wall heat flux distribution.
Originality/value
The proposed scheme is motivated by implicit large eddy simulations that use numerical dissipation as subgrid-scale model. Introducing physical aspects of turbulence into the numerical treatment for RANS simulations is a novel approach.
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Adrian Chun Hin Lai and Adrian Wing-Keung Law
Incineration has become increasingly important in many large cities around the world because of fast urbanization and population growth. The benefits of energy production and…
Abstract
Purpose
Incineration has become increasingly important in many large cities around the world because of fast urbanization and population growth. The benefits of energy production and large reduction in the waste volume to landfills also contribute to its growing adaptation for solid waste management for these cities. At the same time, the environmental impact of the pollutant gases emitted from the incineration process is a common concern for various stakeholders which must be properly addressed. To minimize the pollutant gas emission levels, as well as maximize the energy efficiency, it is critically important to optimize the combustion performance of an incinerator freeboard which would require the development of reliable approaches based on computational fluid dynamics (CFD) modeling. A critical task in the CFD modeling of an incinerator furnace requires the specification of waste characteristics along the moving grate as boundary conditions, which is not available in standard CFD packages at present. This study aims to address this gap by developing a numerical incinerator waste bed model.
Design/methodology/approach
A one-dimensional Lagrangian model for the incineration waste bed has been developed, which can be coupled to the furnace CFD model. The changes in bed mass due to drying, pyrolysis, devolatilization and char oxidation are all included in the model. The mass and concentration of gases produced in these processes through reactions are also predicted. The one-dimensional unsteady energy equations of solid and gas phases, which account for the furnace radiation, conduction, convection and heat of reactions, are solved by the control volume method.
Findings
The Lagrangian model is validated by comparing its prediction with the experimental data in the literature. The predicted waste bed height reduction, temperature profile and gas concentration are in reasonable agreement with the observations.
Originality/value
The simplicity and efficiency of the model makes it ideally suitable to be used for coupling with the computational furnace model to be developed in future (so as to optimize incinerator designs).
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Rene Prieler, Simon Pletzer, Stefan Thusmer, Günther Schwabegger and Christoph Hochenauer
In fire resistance tests (FRTs) of building materials, a crucial criterion to pass the test procedure is to avoid the leakage of the hot flue gases caused by gaps and cracks…
Abstract
Purpose
In fire resistance tests (FRTs) of building materials, a crucial criterion to pass the test procedure is to avoid the leakage of the hot flue gases caused by gaps and cracks occurring due to the thermal exposure. The present study's aim is to calculate the deformation of a steel door, which is embedded within a wall made of bricks, and qualitatively determine the flue gas leakage.
Design/methodology/approach
A computational fluid dynamics/finite element method (CFD/FEM) coupling was introduced representing an intermediate approach between a one-way and a full two-way coupling methodology, leading to a simplified two-way coupling (STWC). In contrast to a full two way-coupling, the heat transfer through the steel door was simulated based on a one-way approach. Subsequently, the predicted temperatures at the door from the one-way simulation were used in the following CFD/FEM simulation, where the fluid flow inside and outside the furnace as well as the deformation of the door were calculated simultaneously.
Findings
The simulation showed large gaps and flue gas leakage above the door lock and at the upper edge of the door, which was in close accordance to the experiment. Furthermore, it was found that STWC predicted similar deformations compared to the one-way coupling.
Originality/value
Since two-way coupling approaches for fluid/structure interaction in fire research are computationally demanding, the number of studies is low. Only a few are dealing with the flue gas exit from rooms due to destruction of solid components. Thus, the present study is the first two-way approach dealing with flue gas leakage due to gap formation.
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