Design and Verification Methodology of Boundary Conditions for Finite Volume Schemes

2012 ◽  
Author(s):  
D. Folkner ◽  
A. Katz ◽  
V. Sankaran
Keyword(s):  
Boundary Conditions ◽  
Finite Volume ◽  
Finite Volume Schemes ◽  
Verification Methodology

scholarly journals Memory efficient finite volume schemes with twisted boundary conditions

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Eduardo I. Bribián ◽  
Jorge Dasilva Golán ◽  
Margarita García Pérez ◽  
Alberto Ramos
Keyword(s):  
Boundary Conditions ◽  
Finite Volume ◽  
Gauge Theories ◽  
Gradient Flow ◽  
Finite Volume Schemes ◽  
Translational Invariance ◽  
Pure Gauge Theory ◽  
Gpu Clusters ◽  
Twisted Boundary Conditions

AbstractIn this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for SU(N) gauge theories consists on a hypercubic box of size $$l^2 \times (Nl)^2$$ l 2 × ( N l ) 2 , a choice motivated by the study of volume independence in large N gauge theories. We argue that this scheme has several advantages that make it particularly suited for precision determinations of the strong coupling, among them translational invariance, an analytic expansion in the coupling and a reduced memory footprint with respect to standard simulations on symmetric lattices, allowing for a more efficient use of current GPU clusters. We test this scheme numerically with a determination of the $$\Lambda $$ Λ parameter in the SU(3) pure gauge theory. We show that the use of an asymmetric geometry has no significant impact in the size of scaling violations, obtaining a value $$\Lambda _{\overline{\mathrm{MS}}}\sqrt{8 t_0} =0.603(17)$$ Λ MS ¯ 8 t 0 = 0.603 ( 17 ) in good agreement with the existing literature. The role of topology freezing, that is relevant for the determination of the coupling in this particular scheme and for large N applications, is discussed in detail.

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>

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