scholarly journals A Forward Time Stepping Heat Conduction Model for Spot Melt Additive Manufacturing

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
B. Stump ◽  
A. Plotkowski
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Analytic Solution ◽  
Dimensional Space ◽  
Mathematical Formulation ◽  
Finite Volume Methods ◽  
Analytic Solutions ◽  
Conduction Model ◽  
Time Stepping ◽  
Speed And Accuracy

Abstract Solidification dynamics are crucial for determining microstructure development in additively manufactured parts. Multiphysics models based on finite element or finite volume methods may help gain insight for complicated phenomena such as fluid flow, keyholing, and porosity but are too computationally expensive to use for simulating actual builds. Recent analytic and semi-analytic solutions for moving heat sources in a semi-infinite three-dimensional space provide a way to accurately estimate the solidification conditions for entire builds. The downside to these methods is that, unlike finite element or finite volume methods, they cannot use the temperature distribution of the previous timesteps to march the solution forward in time. This paper provides the mathematical formulation and implementation of a forward time stepping (FTS) approach to an existing semi-analytic solution. The speed and accuracy of the two methods are then compared for various scan patterns. The result is that, for spot melts, the forward time-stepping model provides improvements in both speed and accuracy. This is especially true for longer simulations, where the simulation can be orders of magnitude faster. The longest simulation analyzed in this paper was roughly 30× faster when using the forward time-stepping model versus the straightforward implementation of the semi-analytic solution.

Transport Schemes in GungHo

2021 ◽  
Author(s):  
James Kent
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Mixed Finite Element ◽  
Method Of Lines ◽  
Finite Volume Methods ◽  
Kutta Method ◽  
Finite Volume Schemes ◽  
Dynamical Core ◽  
Runge Kutta Method ◽  
The Stability

<p>GungHo is the mixed finite-element dynamical core under development by the Met Office. A key component of the dynamical core is the transport scheme, which advects density, temperature, moisture, and the winds, throughout the atmosphere. Transport in GungHo is performed by finite-volume methods, to ensure conservation of certain quantaties. There are a range of different finite-volume schemes being considered for transport, including the Runge-Kutta/method-of-lines and COSMIC/Lin-Rood schemes. Additional horizontal/vertical splitting approaches are also under consideration, to improve the stability aspects of the model. Here we discuss these transport options and present results from the GungHo framework, featuring both prescribed velocity advection tests and full dry dynamical core tests. </p>

scholarly journals Mixed finite element-finite volume methods

2010 ◽  
Vol 17 (3) ◽  
pp. 385-410
Author(s):  
Khadija Zine Dine ◽  
Naceur Achtaich ◽  
Mohamed Chagdali
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Mixed Finite Element ◽  
Finite Volume Methods

scholarly journals Finite volume simulation of unsteady water pipe flow

2014 ◽  
Vol 7 (2) ◽  
pp. 83-92 ◽  
Author(s):  
J. Fernández-Pato ◽  
P. García-Navarro
Keyword(s):  
Numerical Simulation ◽  
Numerical Model ◽  
Finite Volume ◽  
Water Pressure ◽  
Laboratory Data ◽  
Network Models ◽  
Finite Volume Methods ◽  
Analytic Solutions ◽  
Surface Flow ◽  
Pipe Networks

Abstract. The most commonly used hydraulic network models used in the drinking water community exclusively consider fully filled pipes. However, water flow numerical simulation in urban pipe systems may require to model transitions between surface flow and pressurized flow in steady and transient situations. The governing equations for both flow types are different and this must be taken into account in order to get a complete numerical model for solving dynamically transients. In this work, a numerical simulation tool is developed, capable of simulating pipe networks mainly unpressurized, with isolated points of pressurization. For this purpose, the mathematical model is reformulated by means of the Preissmann slot method. This technique provides a reasonable estimation of the water pressure in cases of pressurization. The numerical model is based on the first order Roe's scheme, in the frame of finite volume methods. The novelty of the method is that it is adapted to abrupt transient situations, with subcritical and supercritical flows. The validation has been done by means of several cases with analytic solutions or empirical laboratory data. It has also been applied to some more complex and realistic cases, like junctions or pipe networks.

scholarly journals Performance of the Finite Element and Finite Volume Methods for Large Eddy Simulation in Homogeneous Isotropic Turbulence

2010 ◽  
Vol 2 (2) ◽  
pp. 237-249 ◽  
Author(s):  
M. A. Uddin ◽  
C. Kato ◽  
N. Oshima ◽  
M. Tanahashi ◽  
T. Miyauchi
Keyword(s):  
Finite Element ◽  
Large Eddy Simulation ◽  
Finite Volume ◽  
Isotropic Turbulence ◽  
Finite Volume Methods ◽  
Homogeneous Isotropic Turbulence ◽  
Smagorinsky Model ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Better Than

Large eddy simulation (LES) in homogeneous isotropic turbulence is performed by using the Finite element method (FEM) and Finite volume vethod (FVM) and the results are compared to show the performance of FEM and FVM numerical solvers. The validation tests are done by using the standard Smagorinsky model (SSM) and dynamic Smagorinsky model (DSM) for subgrid-scale modeling. LES is performed on a uniformly distributed 643 grids and the Reynolds number is low enough that the computational grid is capable of resolving all the turbulence scales. The LES results are compared with those from direct numerical simulation (DNS) which is calculated by a spectral method in order to assess its spectral accuracy. It is shown that the performance of FEM results is better than FVM results in this simulation. It is also shown that DSM performs better than SSM for both FEM and FVM simulations and it gives good agreement with DNS results in terms of both spatial spectra and decay of the turbulence statistics. Visualization of second invariant, Q, in LES data for both FEM and FVM reveals the existence of distinct, coherent, and tube-like vortical structures somewhat similar to those found in instantaneous flow field computed by the DNS. Keywords: Large eddy simulation; Validation; Smagorinsky model; Dynamic Smagorinsky model; Tube-like vortical structure; Homogeneous isotropic turbulence. © 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.DOI: 10.3329/jsr.v2i2.2582              J. Sci. Res. 2 (2), 237-249 (2010) 

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