Analytical and Numerical Methods for Wave Propagation in Fluid Media

10.1142/5092 ◽  
2002 ◽  
Author(s):  
K Murawski
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Fluid Media

Chebyshev multidomain pseudospectral method to solve cardiac wave equations with rotational anisotropy

2018 ◽  
Vol 09 (04) ◽  
pp. 1850025 ◽  
Author(s):  
Jairo Rodríguez-Padilla ◽  
Daniel Olmos-Liceaga
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Pseudospectral Method ◽  
Finite Difference Schemes ◽  
Cardiac Models ◽  
Computational Resources ◽  
Realistic Geometries

The implementation of numerical methods to solve and study equations for cardiac wave propagation in realistic geometries is very costly, in terms of computational resources. The aim of this work is to show the improvement that can be obtained with Chebyshev polynomials-based methods over the classical finite difference schemes to obtain numerical solutions of cardiac models. To this end, we present a Chebyshev multidomain (CMD) Pseudospectral method to solve a simple two variable cardiac models on three-dimensional anisotropic media and we show the usefulness of the method over the traditional finite differences scheme widely used in the literature.

scholarly journals Wave Propagation Across Acoustic/Biot’s Media: A Finite-Difference Method

2013 ◽  
Vol 13 (4) ◽  
pp. 985-1012 ◽  
Author(s):  
Guillaume Chiavassa ◽  
Bruno Lombard
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Heterogeneous Media ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Compressional Wave ◽  
Interface Conditions ◽  
Immersed Interface Method ◽  
Fluid Medium ◽  
Strang Splitting

AbstractNumerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid/poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot’s equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect pores. Well-posedness of the initial-boundary value problem is proven. Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context: a fourth-order ADER scheme with Strang splitting for time- marching; a space-time mesh-refinement to capture the slow compressional wave predicted by Biot’s theory; and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution. Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions, demonstrating the accuracy of the approach.

Numerical Methods for Two-Fluid Dispersive Fast MHD Phenomena

2011 ◽  
Vol 10 (1) ◽  
pp. 183-215 ◽  
Author(s):  
Bhuvana Srinivasan ◽  
Ammar Hakim ◽  
Uri Shumlak
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Discontinuous Galerkin ◽  
Equation System ◽  
Source Terms ◽  
Phase Errors ◽  
Wave Propagation Method ◽  
Fluid Equations ◽  
Runge Kutta ◽  
Two Fluid

AbstractThe finite volume wave propagation method and the finite element Runge-Kutta discontinuous Galerkin (RKDG) method are studied for applications to balance laws describing plasma fluids. The plasma fluid equations explored are dispersive and not dissipative. The physical dispersion introduced through the source terms leads to the wide variety of plasma waves. The dispersive nature of the plasma fluid equations explored separates the work in this paper from previous publications. The linearized Euler equations with dispersive source terms are used as a model equation system to compare the wave propagation and RKDG methods. The numerical methods are then studied for applications of the full two-fluid plasma equations. The two-fluid equations describe the self-consistent evolution of electron and ion fluids in the presence of electromagnetic fields. It is found that the wave propagation method, when run at a CFL number of 1, is more accurate for equation systems that do not have disparate characteristic speeds. However, if the oscillation frequency is large compared to the frequency of information propagation, source splitting in the wave propagation method may cause phase errors. The Runge-Kutta discontinuous Galerkin method providesmore accurate results for problems near steady-state aswell as problems with disparate characteristic speeds when using higher spatial orders.

The Buckling Mechanism of Square Tube Subjected to the Impact of a Mass

2014 ◽  
Vol 624 ◽  
pp. 267-271
Author(s):  
Zhu Hua Tan ◽  
Bo Zhang ◽  
Peng Cheng Zhai
Keyword(s):  
Numerical Simulation ◽  
Wave Propagation ◽  
Numerical Methods ◽  
Stress Wave ◽  
Significant Influence ◽  
Strain Localization ◽  
Stress Wave Propagation ◽  
Low Velocity ◽  
Buckling Modes ◽  
The Impact

The dynamic response of the square tube subjected to the impact of a mass was investigated by using experimental and numerical methods. The square tube was impacted by a mass at the velocity ranging from 5.09 m/s to 12.78 m/s, and different progressive buckling modes were obtained. The numerical simulation was also carried out to analyze the buckling mechanism of the square tube. The results show that there is obvious stress wave propagation and strain localization in the tube, which has a significant influence on the buckling mechanism of the tube. The stress wave and inertia of the mass play different roles at various impact velocities. And buckling mechanism at low velocity is mainly caused by stress wave, whereas the buckling mechanism at high velocity is resulted from the inertial of the mass.

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