Multiscale Simulations of Heat Transfer and Fluid Flow Problems

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Ya-Ling He ◽  
Wen-Quan Tao
Keyword(s):  
Multiscale Simulation ◽  
Multiscale Simulations ◽  
Research Needs ◽  
Mesoscale Simulation ◽  
Numerical Examples ◽  
Multiscale Problems ◽  
Flow Problems ◽  
Reconstruction Operator ◽  
Entire Flow ◽  
Numerical Approaches

The multiscale problems in the thermal and fluid science are classified into two categories: multiscale process and multiscale system. The meanings of the two categories are described. Examples are provided for multiscale process and multiscale system. In this paper, focus is put on the simulation of multiscale process. The numerical approaches for multiscale processes have two categories: one is the usage of a general governing equation and solving the entire flow field involving a variation of several orders in characteristic geometric scale. The other is the so-called “solving regionally and coupling at the interfaces.” In this approach, the processes at different length levels are simulated by different numerical methods and then information is exchanged at the interfaces between different regions. The key point is the establishment of the reconstruction operator, which transforms the data of few variables of macroscopic computation to a large amount of variables of microscale or mesoscale simulation. Six numerical examples of multiscale simulation are presented. Finally, some research needs are proposed.

scholarly journals A Mathematical Model and Numerical Solution of a Boundary Value Problem for a Multi-Structure Plate

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 244 ◽  
Author(s):  
Vildan Yazıcı ◽  
Zahir Muradoğlu
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Transmission Conditions ◽  
Numerical Examples ◽  
Deformation Problem ◽  
The Common ◽  
Plate System ◽  
Structure Plate ◽  
Numerical Approaches

This study examined the deformation problem of a plate system (formed side-by-side) composed of multi-structure plates. It obtained numerical approaches of the transmission conditions on the common border of plates that composed the system. Numerical examples were solved in different boundary and transmission conditions.

scholarly journals Flexible composition and execution of high performance, high fidelity multiscale biomedical simulations

2013 ◽  
Vol 3 (2) ◽  
pp. 20120087 ◽  
Author(s):  
D. Groen ◽  
J. Borgdorff ◽  
C. Bona-Casas ◽  
J. Hetherington ◽  
R. W. Nash ◽  
...  
Keyword(s):  
High Performance ◽  
Multiscale Simulation ◽  
High Fidelity ◽  
Biomedical Domain ◽  
Multiscale Simulations ◽  
Total Execution Time ◽  
Stent Restenosis ◽  
Single Scale ◽  
Wide Range ◽  
In Stent Restenosis

Multiscale simulations are essential in the biomedical domain to accurately model human physiology. We present a modular approach for designing, constructing and executing multiscale simulations on a wide range of resources, from laptops to petascale supercomputers, including combinations of these. Our work features two multiscale applications, in-stent restenosis and cerebrovascular bloodflow, which combine multiple existing single-scale applications to create a multiscale simulation. These applications can be efficiently coupled, deployed and executed on computers up to the largest (peta) scale, incurring a coupling overhead of 1–10% of the total execution time.

Mathematical Basis of G Spaces

2016 ◽  
Vol 13 (04) ◽  
pp. 1641007 ◽  
Author(s):  
Meng Chen ◽  
Ming Li ◽  
G. R. Liu
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Weak Formulation ◽  
Mathematical Basis ◽  
Numerical Examples ◽  
Interpolation Methods ◽  
Point Interpolation ◽  
Theoretical Frame ◽  
Lower Boundedness ◽  
Numerical Approaches

This paper represents some basic mathematic theories for G[Formula: see text] spaces of functions that can be used for weakened weak (W2) formulations, upon which the smoothed finite element methods (S-FEMs) and the smoothed point interpolation methods (S-PIMs) are based for solving mechanics problems. We first introduce and prove properties of G[Formula: see text] spaces, such as the lower boundedness and convergence of the norms, which are in contrast with H1spaces. We then prove the equivalence of the Gsnorms and its corresponding semi-norms. These mathematic theories are important and essential for the establishment of theoretical frame and the development of relevant numerical approaches. Finally, numerical examples are presented by using typical S-FEM models known as the NS-FEM and [Formula: see text]S-FEM to examine the properties of a smoothed method based on Gsspaces, in comparison with the standard FEM with weak formulation.

Multiscale Simulation of Knudsen-Pump Channel Flows

2014 ◽  
Author(s):  
Alexander Patronis ◽  
Duncan A. Lockerby
Keyword(s):  
Rarefied Gas ◽  
Hybrid Approach ◽  
Multiscale Simulation ◽  
Single Stage ◽  
Gas Flows ◽  
Multiscale Simulations ◽  
Molecular Approach ◽  
Rarefied Gas Flows ◽  
Knudsen Compressors ◽  
Knudsen Pump

This paper describes the development and application of an efficient hybrid continuum-molecular approach for simulating non-isothermal, low-speed, internal rarefied gas flows, and its application to flows in Knudsen compressors. The method is an extension of the hybrid approach presented by Patronis et al. (2013) [J. Comp. Phys., 255, pp 558–571], which is based on the framework originally proposed by Borg et al. (2013) [J. Comp. Phys., 233, pp 400–413] for the simulation of micro/nano flows of high-aspect-ratio. The efficiency of the multiscale method allows the investigation of alternative Knudsen-compressor configurations to be undertaken. We characterise the effectiveness of the single-stage Knudsen-compressor channel by the pressure differential that can be achieved between two connected reservoirs, for a given temperature difference. Our multiscale simulations indicate that the efficiency of the single-stage Knudsen compressor is robust to modifications of the streamwise temperature variation.

Free Vibration of Doubly Curved Thin Shells

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
April Bryan
Keyword(s):  
Differential Equation ◽  
Vibration Analysis ◽  
Equation Of Motion ◽  
Thin Shells ◽  
Numerical Examples ◽  
Normal Coordinates ◽  
Spatial Equation ◽  
Doubly Curved ◽  
Analytical Approaches ◽  
Numerical Approaches

While several numerical approaches exist for the vibration analysis of thin shells, there is a lack of analytical approaches to address this problem. This is due to complications that arise from coupling between the midsurface and normal coordinates in the transverse differential equation of motion (TDEM) of the shell. In this research, an Uncoupling Theorem for solving the TDEM of doubly curved, thin shells with equivalent radii is introduced. The use of the uncoupling theorem leads to the development of an uncoupled transverse differential of motion for the shells under consideration. Solution of the uncoupled spatial equation results in a general expression for the eigenfrequencies of these shells. The theorem is applied to four shell geometries, and numerical examples are used to demonstrate the influence of material and geometric parameters on the eigenfrequencies of these shells.

The Phase Field Method: Mesoscale Simulation Aiding Material Discovery

2019 ◽  
Vol 49 (1) ◽  
pp. 79-102 ◽  
Author(s):  
Michael R. Tonks ◽  
Larry K. Aagesen
Keyword(s):  
Microstructure Evolution ◽  
Phase Field ◽  
Model Development ◽  
Field Method ◽  
Mesoscale Modeling ◽  
Atomic Scale ◽  
Phase Field Method ◽  
Mesoscale Simulation ◽  
Initial Research ◽  
Numerical Approaches

Mesoscale modeling and simulation approaches provide a bridge from atomic-scale methods to the macroscale. The phase field (PF) method has emerged as a powerful and popular tool for mesoscale simulation of microstructure evolution, and its use is growing at an ever-increasing rate. While initial research using the PF method focused on model development, as it has matured it has been used more and more for material discovery. In this review we focus on applying the PF method for material discovery. We start with a brief summary of the method, including numerical approaches for solving the PF equations. We then give seven examples of the application of the PF method for material discovery. We also discuss four barriers to its use for material discovery and provide approaches for how these barriers can be overcome. Finally, we detail four lessons that can be learned from the examples on how best to apply the PF method for material discovery.

scholarly journals Computationally efficient model of myocardial electromechanics for multiscale simulations

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0255027
Author(s):  
Fyodor Syomin ◽  
Anna Osepyan ◽  
Andrey Tsaturyan
Keyword(s):  
Interstimulus Interval ◽  
Cardiac Electrophysiology ◽  
Multiscale Simulation ◽  
Multiscale Simulations ◽  
Muscle Strain ◽  
Computationally Efficient ◽  
Time Step ◽  
Contraction Coupling ◽  
The Impact ◽  
High Stimulation Frequency

A model of myocardial electromechanics is suggested. It combines modified and simplified versions of previously published models of cardiac electrophysiology, excitation-contraction coupling, and mechanics. The mechano-calcium and mechano-electrical feedbacks, including the strain-dependence of the propagation velocity of the action potential, are also accounted for. The model reproduces changes in the twitch amplitude and Ca2+-transients upon changes in muscle strain including the slow response. The model also reproduces the Bowditch effect and changes in the twitch amplitude and duration upon changes in the interstimulus interval, including accelerated relaxation at high stimulation frequency. Special efforts were taken to reduce the stiffness of the differential equations of the model. As a result, the equations can be integrated numerically with a relatively high time step making the model suitable for multiscale simulation of the human heart and allowing one to study the impact of myocardial mechanics on arrhythmias.

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