Two-Dimensional Simulation of Wave Propagation in a Three-Pipe Junction

2000 ◽  
Vol 122 (4) ◽  
pp. 549-555 ◽  
Author(s):  
R. J. Pearson ◽  
M. D. Bassett ◽  
P. Batten ◽  
D. E. Winterbone
Keyword(s):  
Wave Propagation ◽  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Finite Volume Scheme ◽  
Two Dimensional ◽  
Action Simulation ◽  
Pressure Time ◽  
Time Histories ◽  
Dimensional Simulation ◽  
Measured Pressure

The modelling of wave propagation in complex pipe junctions is one of the biggest challenges for simulation codes, particularly those applied to flows in engine manifolds. In the present work an inviscid two-dimensional model, using an advanced numerical scheme, has been applied to the simulation of shock-wave propagation through a three-pipe junction; the results are compared with corresponding schlieren images and measured pressure-time histories. An approximate Riemann solver is used in the shock-capturing finite volume scheme and the influence of the order of accuracy of the solver and the use of adaptive mesh refinement are investigated. The code can successfully predict the evolution and reflection of the wave fronts at the junctions whilst the run time is such as to make it feasible to include such a model as a local multi-dimensional region within a one-dimensional wave-action simulation of flow in engine manifolds. [S0742-4795(00)01304-1]

scholarly journals Accelerating numerical wave propagation using wavefield adapted meshes. Part I: forward and adjoint modelling

2020 ◽  
Vol 221 (3) ◽  
pp. 1580-1590 ◽  
Author(s):  
M van Driel ◽  
C Boehm ◽  
L Krischer ◽  
M Afanasiev
Keyword(s):  
Wave Propagation ◽  
Adaptive Mesh Refinement ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Model Space ◽  
Adaptive Mesh ◽  
Order Of Magnitude ◽  
Speed Up ◽  
Adjoint Modelling ◽  
The Waves

SUMMARY An order of magnitude speed-up in finite-element modelling of wave propagation can be achieved by adapting the mesh to the anticipated space-dependent complexity and smoothness of the waves. This can be achieved by designing the mesh not only to respect the local wavelengths, but also the propagation direction of the waves depending on the source location, hence by anisotropic adaptive mesh refinement. Discrete gradients with respect to material properties as needed in full waveform inversion can still be computed exactly, but at greatly reduced computational cost. In order to do this, we explicitly distinguish the discretization of the model space from the discretization of the wavefield and derive the necessary expressions to map the discrete gradient into the model space. While the idea is applicable to any wave propagation problem that retains predictable smoothness in the solution, we highlight the idea of this approach with instructive 2-D examples of forward as well as inverse elastic wave propagation. Furthermore, we apply the method to 3-D global seismic wave simulations and demonstrate how meshes can be constructed that take advantage of high-order mappings from the reference coordinates of the finite elements to physical coordinates. Error level and speed-ups are estimated based on convergence tests with 1-D and 3-D models.

Gaseous Deflagration in Piping: Part 1 — Experimental Observations

2017 ◽  
Author(s):  
Thomas C. Ligon ◽  
David J. Gross ◽  
John C. Minichiello
Keyword(s):  
High Speed ◽  
Structural Response ◽  
Analysis And Design ◽  
Flame Acceleration ◽  
Pressure Time ◽  
Piping Systems ◽  
Time Histories ◽  
Short Test ◽  
Semi Empirical ◽  
Measured Pressure

The focus of this paper is on gaseous deflagration in piping systems and the corresponding implications on piping analysis and design. Unlike stable detonations that propagate at a constant speed and whose pressure-time histories can in some cases be predicted analytically, deflagration flame speeds and pressure-time histories are transient and depend on both the gas mixture and geometry of the pipe. This paper presents pressure and pipe strain data from gaseous deflagration experiments in long and short test apparatuses fabricated from either 2-inch or 4-inch diameter pipes. These data are used to demonstrate a spectrum of measured pressure-time histories and corresponding pipe response. It is concluded that deflagrations can be categorized as either “high” or “slow” speed with respect to pipe response. Slow deflagrations can be treated as quasi-static pressurizations, but high speed deflagrations can generate shock waves that dynamically excite the pipe. The existence of a transition from quasi-static to dynamic response has ramifications in regards to piping structural analysis and design, and a method for predicting the expected deflagration structural response using a semi-empirical flame acceleration model is proposed.

Logically rectangular finite volume methods with adaptive refinement on the sphere

2009 ◽  
Vol 367 (1907) ◽  
pp. 4483-4496 ◽  
Author(s):  
Marsha J. Berger ◽  
Donna A. Calhoun ◽  
Christiane Helzel ◽  
Randall J. LeVeque
Keyword(s):  
Finite Volume ◽  
Shallow Water Equations ◽  
Adaptive Mesh Refinement ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Finite Volume Methods ◽  
Adaptive Refinement ◽  
Two Dimensional ◽  
Equilibrium Solutions ◽  
Courant Number

The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the G eo C law software and demonstrate well-balanced methods that exactly maintain equilibrium solutions, such as shallow water equations for an ocean at rest over arbitrary bathymetry.

scholarly journals Adaptive Mesh Refinement and Adaptive Time Integration for Electrical Wave Propagation on the Purkinje System

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Wenjun Ying ◽  
Craig S. Henriquez
Keyword(s):  
Wave Propagation ◽  
Adaptive Algorithm ◽  
Adaptive Mesh Refinement ◽  
Method Of Lines ◽  
Adaptive Mesh ◽  
Membrane Properties ◽  
Computational Domain ◽  
Linear Diffusion ◽  
Splitting Technique ◽  
Purkinje System

A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented.

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