scholarly journals The QUICK scheme is a third‐order finite‐volume scheme with point‐valued numerical solutions

2021 ◽  
Author(s):  
Hiroaki Nishikawa
Keyword(s):  
Finite Volume ◽  
Numerical Solutions ◽  
Finite Volume Scheme ◽  
Third Order ◽  
Volume Scheme ◽  
Quick Scheme

scholarly journals A Global Multimoment Constrained Finite-Volume Scheme for Advection Transport on the Hexagonal Geodesic Grid

2011 ◽  
Vol 140 (3) ◽  
pp. 941-955 ◽  
Author(s):  
Chungang Chen ◽  
Juzhong Bin ◽  
Feng Xiao
Keyword(s):  
Numerical Model ◽  
Finite Volume ◽  
Present Method ◽  
Evolution Equations ◽  
Present Model ◽  
Spherical Geometry ◽  
Finite Volume Scheme ◽  
Third Order ◽  
Order Accuracy ◽  
Volume Scheme

Abstract A third-order numerical model is developed for global advection transport computation. The multimoment constrained finite-volume scheme has been implemented to the hexagonal geodesic grid for spherical geometry. Two kinds of moments (i.e., point value and volume-integrated average) are used as the constraint conditions to derive the time evolution equations to update the computational variables, which are the values defined at the specified points over each mesh element in the present model. The numerical model has rigorous numerical conservation and third-order accuracy. One of the major merits of the present method is that it does not explicitly involve numerical quadrature, which leads to great convenience in accurately computing curved geometry and source terms. The present paper provides an accurate and practical formulation for advection calculation in the hexagonal-type geodesic grid.

scholarly journals Convergence of a finite volume scheme for the compressible Navier–Stokes system

2019 ◽  
Vol 53 (6) ◽  
pp. 1957-1979 ◽  
Author(s):  
Eduard Feireisl ◽  
Mária Lukáčová-Medvid’ová ◽  
Hana Mizerová ◽  
Bangwei She
Keyword(s):  
Finite Volume ◽  
Numerical Experiments ◽  
Stokes System ◽  
Numerical Solutions ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Benchmark Tests ◽  
Stability And Consistency ◽  
Theoretical Results

We study convergence of a finite volume scheme for the compressible (barotropic) Navier–Stokes system. First we prove the energy stability and consistency of the scheme and show that the numerical solutions generate a dissipative measure-valued solution of the system. Then by the dissipative measure-valued-strong uniqueness principle, we conclude the convergence of the numerical solution to the strong solution as long as the latter exists. Numerical experiments for standard benchmark tests support our theoretical results.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

scholarly journals A 3D finite volume scheme for the simulation of edge plasma in Tokamaks

2013 ◽  
Vol 43 ◽  
pp. 164-179
Author(s):  
M. Bilanceri ◽  
L. Combe ◽  
H. Guillard ◽  
B. Nkonga ◽  
A. Sangam
Keyword(s):  
Finite Volume ◽  
Edge Plasma ◽  
Finite Volume Scheme ◽  
Volume Scheme
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