Computation of Sub-Micron Thermal Transport Using an Unstructured Finite Volume Method

2002 ◽  
Vol 124 (6) ◽  
pp. 1176-1181 ◽  
Author(s):  
J. Y. Murthy ◽  
S. R. Mathur
Keyword(s):  
Finite Volume ◽  
Isotropic Scattering ◽  
Finite Volume Scheme ◽  
Boltzmann Transport ◽  
Linear Set ◽  
Volume Scheme ◽  
Relaxation Time Approximation ◽  
Fully Implicit ◽  
Volume Method ◽  
Unstructured Finite Volume Method

An unstructured finite volume scheme is applied to the solution of sub-micron heat conduction problems. The phonon Boltzmann transport equation (BTE) in the relaxation time approximation is considered. The similarity between the radiative transfer equation (RTE) and the BTE is exploited in developing a finite volume scheme for the BTE. The spatial domain is divided into arbitrary unstructured polyhedra, the angular domain into control angles, and the frequency domain into frequency bands, and conservation equations for phonon energy are written. The unsteady wave propagation term, not usually present in thermal radiation problems, is differentiated using a fully implicit scheme. A sequential multigrid scheme is applied to solve the nominally linear set. Isotropic scattering due to a variety of mechanisms such as impurity and Umklapp scattering is considered. The numerical scheme is applied to a variety of sub-micron conduction problems, both unsteady and steady. Favorable comparison is found with the published literature and with exact solutions.

Computation of Sub-Micron Thermal Transport Using an Unstructured Finite Volume Method

2001 ◽  
Author(s):  
J. Y. Murthy ◽  
S. R. Mathur
Keyword(s):  
Finite Volume ◽  
Isotropic Scattering ◽  
Finite Volume Scheme ◽  
Boltzmann Transport ◽  
Linear Set ◽  
Volume Scheme ◽  
Relaxation Time Approximation ◽  
Fully Implicit ◽  
Volume Method ◽  
Unstructured Finite Volume Method

Abstract An unstructured finite volume scheme is applied to the solution of sub-micron heat conduction problems. The phonon Boltzmann transport equation (BTE) in the relaxation time approximation is considered. The similarity between the radiative transfer equation (RTE) and the BTE is exploited in developing a finite volume scheme for the BTE. The spatial domain is divided into arbitrary unstructured polyhedra, the angular domain into control angles and the frequency domain into frequency bands and conservation equations for phonon energy are written. The unsteady wave propagation term; not usually present in thermal radiation problems, is differenced using a fully implicit scheme. A sequential multigrid scheme is applied to solve the nominally linear set. Isotropic scattering due to a variety of mechanisms such as impurity and Umklapp scattering is considered. The numerical scheme is applied to a variety of sub-micron conduction problems, both unsteady and steady. Favorable comparison is found with the published literature and with exact solutions.

Multi-Mode Heat Transfer in a Randomly Packed Bed of Cylindrical Rods Using a Finite Volume Scheme

2000 ◽  
Author(s):  
J. Y. Murthy ◽  
S. R. Mathur
Keyword(s):  
Heat Transfer ◽  
Finite Volume ◽  
Packed Bed ◽  
Refractive Indices ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Volume Method ◽  
Periodic Module ◽  
Multi Mode ◽  
Unstructured Finite Volume Method

Abstract In this paper, calculations of mixed-mode heat transfer in beds of randomly-packed cylinders are presented. An unstructured finite volume method is employed. Random packing is addressed by meshing a periodic module, and creating the bed by stacking and random lateral translation of modules. The ability of the finite volume scheme to employ arbitrary polyhedra is exploited in addressing the resulting non-conformal interfaces. Conduction and radiation are considered, but convection is ignored. Results are presented for conducting and semi-transparent cylinders for a range of fluid and solid conductivities and solid refractive indices and establish the viability and versatility of the method.

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.

Numerical Analysis of a Stable Finite Volume Scheme for a Generalized Thermistor Model

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mustapha Ghilani ◽  
El Houssaine Quenjel ◽  
Mohamed Rhoudaf
Keyword(s):  
Weak Solution ◽  
Finite Volume ◽  
Electric Potential ◽  
Discrete Maximum Principle ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Stiffness Coefficients ◽  
Fully Implicit ◽  
The Stability ◽  
Stability Issues

AbstractA generalized thermistor model is discretized thanks to a fully implicit vertex-centered finite volume scheme on simplicial meshes. An assumption on the stiffness coefficients is mandatory to prove a discrete maximum principle on the electric potential. This property is fundamental to handle the stability issues related to the Joule heating term. Then the convergence to a weak solution is established. Finally, numerical results are presented to show the efficiency of the methodology and to illustrate the behavior of the temperature together with the electric potential within the medium.

scholarly journals Effects of mesh loop modes on performance of unstructured finite volume GPU simulations

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Yue Weng ◽  
Xi Zhang ◽  
Xiaohu Guo ◽  
Xianwei Zhang ◽  
Yutong Lu ◽  
...  
Keyword(s):  
Finite Volume ◽  
Data Access ◽  
Data Locality ◽  
Data Dependence ◽  
Speed Up ◽  
Computational Fluid Dynamics Cfd ◽  
Overall Performance ◽  
Volume Method ◽  
Cell Data ◽  
Unstructured Finite Volume Method

AbstractIn unstructured finite volume method, loop on different mesh components such as cells, faces, nodes, etc is used widely for the traversal of data. Mesh loop results in direct or indirect data access that affects data locality significantly. By loop on mesh, many threads accessing the same data lead to data dependence. Both data locality and data dependence play an important part in the performance of GPU simulations. For optimizing a GPU-accelerated unstructured finite volume Computational Fluid Dynamics (CFD) program, the performance of hot spots under different loops on cells, faces, and nodes is evaluated on Nvidia Tesla V100 and K80. Numerical tests under different mesh scales show that the effects of mesh loop modes are different on data locality and data dependence. Specifically, face loop makes the best data locality, so long as access to face data exists in kernels. Cell loop brings the smallest overheads due to non-coalescing data access, when both cell and node data are used in computing without face data. Cell loop owns the best performance in the condition that only indirect access of cell data exists in kernels. Atomic operations reduced the performance of kernels largely in K80, which is not obvious on V100. With the suitable mesh loop mode in all kernels, the overall performance of GPU simulations can be increased by 15%-20%. Finally, the program on a single GPU V100 can achieve maximum 21.7 and average 14.1 speed up compared with 28 MPI tasks on two Intel CPUs Xeon Gold 6132.

Sign in / Sign up

Export Citation Format

Share Document