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.

Monotone Finite Volume Scheme for Three Dimensional Diffusion Equation on Tetrahedral Meshes

2016 ◽  
Vol 21 (1) ◽  
pp. 162-181 ◽  
Author(s):  
Xiang Lai ◽  
Zhiqiang Sheng ◽  
Guangwei Yuan
Keyword(s):  
Diffusion Equation ◽  
Finite Volume ◽  
Three Dimensional ◽  
Finite Volume Scheme ◽  
Order Accuracy ◽  
Volume Scheme ◽  
Tetrahedral Meshes ◽  
Dimensional Diffusion ◽  
Coefficient Problems ◽  
Monotone Finite Volume Scheme

AbstractWe construct a nonlinear monotone finite volume scheme for three-dimensional diffusion equation on tetrahedral meshes. Since it is crucial important to eliminate the vertex unknowns in the construction of the scheme, we present a new efficient eliminating method. The scheme has only cell-centered unknowns and can deal with discontinuous or tensor diffusion coefficient problems on distorted meshes rigorously. The numerical results illustrate that the resulting scheme can preserve positivity on distorted tetrahedral meshes, and also show that our scheme appears to be approximate second-order accuracy for solution.

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 Hydrodynamic-Based Robust Numerical Model for Debris Hazard and Risk Assessment

2021 ◽  
Vol 13 (14) ◽  
pp. 7955
Author(s):  
Yongde Kang ◽  
Jingming Hou ◽  
Yu Tong ◽  
Baoshan Shi
Keyword(s):  
Numerical Model ◽  
Debris Flow ◽  
Finite Volume ◽  
Graphics Processing Unit ◽  
Morphological Changes ◽  
Finite Volume Scheme ◽  
Processing Unit ◽  
Algebraic Equations ◽  
Flow Process ◽  
Computing Technique

Debris flow simulations are important in practical engineering. In this study, a graphics processing unit (GPU)-based numerical model that couples hydrodynamic and morphological processes was developed to simulate debris flow, transport, and morphological changes. To accurately predict the debris flow sediment transport and sediment scouring processes, a GPU-based parallel computing technique was used to accelerate the calculation. This model was created in the framework of a Godunov-type finite volume scheme and discretized into algebraic equations by the finite volume method. The mass and momentum fluxes were computed using the Harten, Lax, and van Leer Contact (HLLC) approximate Riemann solver, and the friction source terms were calculated using the proposed splitting point-implicit method. These values were evaluated using a novel 2D edge-based MUSCL scheme. The code was programmed using C++ and CUDA, which can run on GPUs to substantially accelerate the computation. After verification, the model was applied to the simulation of the debris flow process of an idealized example. The results of the new scheme better reflect the characteristics of the discontinuity of its movement and the actual law of the evolution of erosion and deposition over time. The research results provide guidance and a reference for the in-depth study of debris flow processes and disaster prevention and mitigation.

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