Two new upwind difference schemes for a coupled system of convection–diffusion equations arising from the steady MHD duct flow problems

Hsieh, Pei-Shan; Yang, Suh-Yuh

doi:10.1016/j.jcp.2010.08.034

Cited by 24 publications

(70 citation statements)

References 18 publications

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“…The sensitivities from the initial states to the output (S S S yx 0 ) are found from: Coupled CDR equations typically describe the dynamics of post-harvest storage processes. However, these equations are also used in a wide range of other processes that utilise the laws of conservation of heat and mass (see, for instance, Hsieh & Yang, 2010;Vali, Simonson, Besant, & Mahmood, 2009;Zambra, Munoz, & Moraga, 2015). In the porous medium of a bulk food-storage facility, interaction between the product and the air induces the coupling between the CDR equations that describe temperature in the air and in the food product.…”

Section: Non-linear 1d Cdr Sensitivity Fieldsmentioning

confidence: 99%

Controllability and observability of 2D thermal flow in bulk storage facilities using sensitivity fields

Grubben

Keesman

2017

International Journal of Control

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To control and observe spatially distributed thermal flow systems, the controllable field and observable field around the actuator and sensor are of interest, respectively. For spatially distributed systems, the classical systems theoretical concepts of controllability and observability are, in general, difficult to apply. In this study, sensitivity fields were used to analyse the behaviour from input to state and from initial state to output. For the analysis of controllability and observability, a large-scale, bulk storage facility with coupled thermal flow of air and agro-products was used. Analysis of this system using the classical systems theory results in controllability and observability results that are dependent on the step size of the spatially discretised system. Due to matrix multiplications, inaccurate results are calculated if the step size is too small. Our findings indicate that input-state and initial-state output sensitivity fields provide sufficient information about the controllability and observability of large coupled spatially distributed systems, using finite-dimensional state space representation with small discretisation steps.

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Section: Non-linear 1d Cdr Sensitivity Fieldsmentioning

confidence: 99%

Controllability and observability of 2D thermal flow in bulk storage facilities using sensitivity fields

Grubben

Keesman

2017

International Journal of Control

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“…The MHD flow problem may obtain analytical solution in some special conditions, but it can only be solved numerically in the general situation . In the past several decades, various numerical approximation methods, involving finite element method (FEM) [14][15][16][17][18][19][20][21][22][23], finite difference method (FDM) [7][8][9][10], boundary element method (BEM) [4][5][6], differential quadrature method (DQM) [24], meshfree (meshless) method (MM) [1][2][3], finite volume spectral element method (FVSEM) [25], have been suggested to solve the coupled equations in velocity and magnetic field for the steady magnetohydrodynamic (MHD) duct flow. However, most of them cannot solve the MHD problems with high Ha effectively.…”

Section: Introductionmentioning

confidence: 99%

“…Tian). a transverse magnetic field with the high Ha, some numerical methods such as finite element and finite difference methods have been developed [7,10,17,19,21,26]. In finite element method, the residual-free bubble functions-based finite element method has drawn researchers' attention [17,19,21,26].…”

Section: Introductionmentioning

confidence: 99%

“…Later, based on the residual-free bubbles functions, Hsieh and Yang [19] developed a stabilized least-squares finite element method and obtained the results even for the value of the Ha up to 10 6 . However, it has been found from the numerical results in [7] that the residual-free bubble functions-based finite element methods [19,26] still exhibit some spurious oscillations near the boundary layer regions for the MHD duct flow problems with high Ha. In finite difference method, Hsieh and Yang [7] proposed two new upwind difference schemes with a high stability to solve successfully the MHD duct flow problem at the high Ha.…”

Section: Introductionmentioning

confidence: 99%

“…However, it has been found from the numerical results in [7] that the residual-free bubble functions-based finite element methods [19,26] still exhibit some spurious oscillations near the boundary layer regions for the MHD duct flow problems with high Ha. In finite difference method, Hsieh and Yang [7] proposed two new upwind difference schemes with a high stability to solve successfully the MHD duct flow problem at the high Ha. The upwind difference schemes proposed in [7] are believed that they are not only able to get a reasonable accuracy, but can also resolve high gradients near the layer regions without refining the grid.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exponential high-order compact scheme on nonuniform grids for the steady MHD duct flow problems with high Hartmann numbers

Zhou

Tian

2015

Computer Physics Communications

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A proper orthogonal decomposition variational multiscale meshless interpolating element‐free Galerkin method for incompressible magnetohydrodynamics flow

Abbaszadeh

Dehghan

Navon

2020

Numerical Methods in Fluids

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Summary In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element‐free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced‐order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced‐order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two‐dimensional cases.

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Two new upwind difference schemes for a coupled system of convection–diffusion equations arising from the steady MHD duct flow problems

Cited by 24 publications

References 18 publications

Controllability and observability of 2D thermal flow in bulk storage facilities using sensitivity fields

Controllability and observability of 2D thermal flow in bulk storage facilities using sensitivity fields

Exponential high-order compact scheme on nonuniform grids for the steady MHD duct flow problems with high Hartmann numbers

A proper orthogonal decomposition variational multiscale meshless interpolating element‐free Galerkin method for incompressible magnetohydrodynamics flow

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