scholarly journals Fiber-based modeling and simulation of skeletal muscles

2021 ◽  
Vol 52 (1) ◽  
pp. 1-30
Author(s):  
M. H. Gfrerer ◽  
B. Simeon
Keyword(s):  
Continuum Mechanics ◽  
Skeletal Muscles ◽  
Computational Cost ◽  
Rigid Bodies ◽  
Muscle Model ◽  
Implicit Time ◽  
Cable Model ◽  
One Dimensional ◽  
Time Stepping ◽  
The Hill

AbstractThis paper presents a novel fiber-based muscle model for the forward dynamics of the musculoskeletal system. While bones are represented by rigid bodies, the muscles are taken into account by means of one-dimensional cables that obey the laws of continuum mechanics. In contrast to standard force elements such as the Hill-type muscle model, this approach is close to the real physiology and also avoids the issue of wobbling masses. On the other hand, the computational cost is rather low in comparison with full 3D continuum mechanics simulations. The cable model includes sliding contact between individual fibers as well as between fibers and bones. For the discretization, cubic finite elements are employed in combination with implicit time stepping. Several validation studies and the simulation of a motion scenario for the upper limb demonstrate the potential of the fiber-based approach.

A Numerical Model of In-Channel Pebble Bed Thermal Storage for a Solar Chimney

2012 ◽  
Author(s):  
Brandon Schulte ◽  
O. A. Plumb
Keyword(s):  
Numerical Model ◽  
Present Model ◽  
Thermal Storage ◽  
Implicit Time ◽  
Heat Transfer Characteristics ◽  
Solar Chimney ◽  
Pebble Bed ◽  
One Dimensional ◽  
Time Stepping ◽  
Daily Energy

In this study, solar chimney performance is numerically modeled. Previously published models have considered water bags and natural earth as means to store daytime thermal energy for nighttime operation of the system. The present model considers in-channel pebble bed thermal storage. A one-dimensional, implicit time stepping numerical model is developed to predict solar chimney performance throughout a 24 hour period. The model is partially verified with available experimental data. The daily energy, daily efficiency and heat transfer characteristics of the solar chimney with pebble bed thermal storage are summarized. The numerical simulation showed that by introducing a pebble bed, nightly exit velocities reach 40% of the peak daytime velocity. However, the daily kinetic energy delivered by a solar chimney with pebble bed thermal storage is much less than a traditional solar chimney, suggesting pebble bed thermal storage is more practicable in building heating applications as opposed to power generation.

scholarly journals Efficient estimation of time-mean states of ocean models using 4D-Var and implicit time-stepping

2007 ◽  
Vol 14 (6) ◽  
pp. 777-788
Author(s):  
A. D. Terwisscha van Scheltinga ◽  
H. A. Dijkstra
Keyword(s):  
Ocean Circulation ◽  
Signal To Noise Ratio ◽  
Singular Spectrum Analysis ◽  
Computational Cost ◽  
Ocean Model ◽  
Efficient Estimation ◽  
Implicit Time ◽  
Time Stepping ◽  
High Frequency Variability ◽  
Mean State

Abstract. We propose an efficient method for estimating a time-mean state of an ocean model subject to given observations using implicit time-stepping. The new method uses (i) an implicit implementation of the 4D-Var method to fit the model trajectory to the observations, and (ii) a pre-processor which applies a multi-channel singular spectrum analysis to enhance the signal-to-noise ratio of the observational data and to filter out the high frequency variability. This approach enables one to estimate the time-mean model state using larger time-steps than is possible with an explicit model. The performance of the method is presented for two test cases within a barotropic quasi-geostrophic nonlinear model of the wind-driven double-gyre ocean circulation. The method turns out to be accurate and, in comparison with the time-mean state computed with an explicit version of the model, relatively cheap in computational cost.

IMPROVED ACCURACY FOR LOCALLY ONE-DIMENSIONAL METHODS FOR PARABOLIC EQUATIONS

2001 ◽  
Vol 11 (09) ◽  
pp. 1563-1579 ◽  
Author(s):  
JIM DOUGLAS ◽  
SEONGJAI KIM
Keyword(s):  
Parabolic Equations ◽  
Wave Equations ◽  
Computational Cost ◽  
Implicit Time ◽  
Differential Problem ◽  
Time Stepping ◽  
Backward Euler ◽  
The Cost ◽  
Improved Accuracy ◽  
Crank Nicolson

Classical alternating direction (AD) and fractional step (FS) methods for parabolic equations, based on some standard implicit time-stepping procedure such as Crank–Nicolson, can have errors associated with the AD or FS perturbations that are much larger than the errors associated with the underlying time-stepping procedure. We show that minor modifications in the AD and FS procedures can virtually eliminate the perturbation errors at an additional computational cost that is less than 10% of the cost of the original AD or FS method. Moreover, after these modifications, the AD and FS procedures produce identical approximations of the solution of the differential problem. It is also shown that the same perturbation of the Crank–Nicolson procedure can be obtained with AD and FS methods associated with the backward Euler time-stepping scheme. An application of the same concept is presented for second-order wave equations.

Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
R. Maffulli ◽  
L. He ◽  
P. Stein ◽  
G. Marinescu
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Time Derivative ◽  
Computational Cost ◽  
Strong Impact ◽  
Time Step ◽  
Time Stepping ◽  
Adaptive Time ◽  
Fully Coupled ◽  
Adaptive Time Stepping

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

A Dynamic Adaptive Wavelet Method for Solution of the Schrodinger Equation

2015 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
Ratikanta Behera ◽  
Mani Mehra
Keyword(s):  
Schrödinger Equation ◽  
Computational Efficiency ◽  
Schrodinger Equation ◽  
Computational Cost ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
One Dimensional ◽  
Grid Adaptation ◽  
Adaptive Wavelet Method

In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based on spherical wavelet over an optimal spherical geodesic grid. The method is applied to the solution of Schrodinger equation for computational efficiency and achieve accuracy with controlling spatial grid adaptation — high resolution computations are performed only in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Thereupon the dynamic adaptive wavelet method is useful to analyze local structure of solution with very less number of computational cost than any other methods. The prowess and computational efficiency of the adaptive wavelet method is demonstrated for the solution of Schrodinger equation on one-dimensional, two-dimensional and on the sphere.

Analysis of Complex Structures Coupling Variable Kinematics One-Dimensional Models

2014 ◽  
Author(s):  
Erasmo Carrera ◽  
Enrico Zappino
Keyword(s):  
Mechanical Design ◽  
Computational Cost ◽  
Advanced Materials ◽  
Complex Structures ◽  
Displacement Fields ◽  
One Dimensional ◽  
Classical Models ◽  
Kinematic Models ◽  
Carrera Unified Formulation ◽  
Dimensional Models

One-dimensional models are widely used in mechanical design. Classical models, Euler-Bernoulli or Timoshenko, ensure a low computational cost but are limited by their assumptions, many refined models were proposed to overcome these limitations and extend one-dimensional models at the analysis of complex geometries or advanced materials. In this work a new approach is proposed to couple different kinematic models. A new finite element is introduced in order to connect one-dimensional elements with different displacement fields. The model is derived in the frameworks of the Carrera Unified Formulation (CUF), therefore the formulation can be written in terms of fundamental nuclei. The results show that the use variable kinematic models allows the computational costs to be reduced without reduce the accuracy, moreover, refined-one dimensional models can be used in the analysis of complex structures.

scholarly journals Wave Propagation in Thin-Walled Aortic Analogues

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
C. G. Giannopapa ◽  
J. M. B. Kroot ◽  
A. S. Tijsseling ◽  
M. C. M. Rutten ◽  
F. N. van de Vosse
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Frequency Domain ◽  
Analytical Model ◽  
Viscoelastic Properties ◽  
Numerical Models ◽  
Computational Cost ◽  
One Dimensional ◽  
Arterial Blood

Research on wave propagation in liquid filled vessels is often motivated by the need to understand arterial blood flows. Theoretical and experimental investigation of the propagation of waves in flexible tubes has been studied by many researchers. The analytical one-dimensional frequency domain wave theory has a great advantage of providing accurate results without the additional computational cost related to the modern time domain simulation models. For assessing the validity of analytical and numerical models, well defined in vitro experiments are of great importance. The objective of this paper is to present a frequency domain analytical model based on the one-dimensional wave propagation theory and validate it against experimental data obtained for aortic analogs. The elastic and viscoelastic properties of the wall are included in the analytical model. The pressure, volumetric flow rate, and wall distention obtained from the analytical model are compared with experimental data in two straight tubes with aortic relevance. The analytical results and the experimental measurements were found to be in good agreement when the viscoelastic properties of the wall are taken into account.

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