A class of finite volume schemes of arbitrary order on nonuniform meshes

2013 ◽  
Vol 30 (5) ◽  
pp. 1614-1632
Author(s):  
Qinghui Zhang ◽  
Qingsong Zou
Keyword(s):  
Finite Volume ◽  
Arbitrary Order ◽  
Finite Volume Schemes ◽  
Nonuniform Meshes

Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows

2006 ◽  
Vol 213 (2) ◽  
pp. 474-499 ◽  
Author(s):  
Sebastian Noelle ◽  
Normann Pankratz ◽  
Gabriella Puppo ◽  
Jostein R. Natvig
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Arbitrary Order ◽  
Finite Volume Schemes ◽  
Order Of Accuracy ◽  
Water Flows ◽  
Shallow Water Flows

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>

MOMENT PRESERVING FINITE VOLUME SCHEMES FOR SOLVING POPULATION BALANCE EQUATIONS INCORPORATING AGGREGATION, BREAKAGE, GROWTH AND SOURCE TERMS

2013 ◽  
Vol 23 (07) ◽  
pp. 1235-1273 ◽  
Author(s):  
RAJESH KUMAR ◽  
JITENDRA KUMAR ◽  
GERALD WARNECKE
Keyword(s):  
Finite Volume ◽  
Population Balance ◽  
Coupled Processes ◽  
Source Terms ◽  
Balance Equations ◽  
Finite Volume Schemes ◽  
Average Technique ◽  
Population Balance Equations ◽  
Moment Preservation ◽  
First Moment

In this work we present some moment preserving finite volume schemes (FVS) for solving population balance equations. We are considering unified numerical methods to simultaneous aggregation, breakage, growth and source terms, e.g. for nucleation. The criteria for the preservation of different moments are given. The property of conservation is a special case of preservation. First we present a FVS which shows the preservation with respect to one-moment depending upon the processes under consideration. In case of the aggregation and breakage it satisfies first-moment preservation whereas for the growth and nucleation we observe zeroth-moment preservation. This is due to the well-known property of conservativity of FVS. However, coupling of all the processes shows no preservation for any moments. To overcome this issue, we reformulate the cell average technique into a conservative formulation which is coupled together with a modified upwind scheme to give moment preservation with respect to the first two-moments for all four processes under consideration. This allows for easy coupling of these processes. The preservation is proven mathematically and verified numerically. The numerical results for the first two-moments are verified for various coupled processes where analytical solutions are available.

scholarly journals Arbitrary Order Finite Volume Well-Balanced Schemes for the Euler Equations with Gravity

2019 ◽  
Vol 41 (2) ◽  
pp. A695-A721 ◽  
Author(s):  
C. Klingenberg ◽  
G. Puppo ◽  
M. Semplice
Keyword(s):  
Euler Equations ◽  
Finite Volume ◽  
Arbitrary Order
Sign in / Sign up

Export Citation Format

Share Document