| 1. |
- Arndt, Daniel, et al.
(author)
-
The deal. II library, Version 9.3
- 2021
-
In: Journal of Numerical Mathematics. - : Walter de Gruyter. - 1570-2820 .- 1569-3953. ; 29:3, s. 171-186
-
Journal article (peer-reviewed)abstract
- This paper provides an overview of the new features of the finite element library deal . II, version 9.3.
|
|
| 2. |
- Arndt, Daniel, et al.
(author)
-
The deal.II library, Version 9.4
- 2022
-
In: Journal of Numerical Mathematics. - : Walter de Gruyter. - 1570-2820 .- 1569-3953. ; 30:3, s. 231-246
-
Journal article (peer-reviewed)abstract
- This paper provides an overview of the new features of the finite element library deal.II, version 9.4.
|
|
| 3. |
- Axelsson, Owe, et al.
(author)
-
Numerical and computational efficiency of solvers for two-phase problems
- 2012
-
Reports (other academic/artistic)abstract
- We consider two-phase flow problems, modelled by the Cahn-Hilliard equation. In our work, the nonlinear fourth-order equation is decomposed into a system of two second-order equations for the concentration and the chemical potential.We analyse solution methods based on an approximate two-by-two block factorization of the Jacobian of the nonlinear discrete problem. We propose a preconditioning technique that reduces the problem of solving the non-symmetric discrete Cahn-Hilliard system to the problem of solving systems with symmetric positive definite matrices where off-the-shelf multilevel and multigrid algorithms are directly applicable. The resulting solution methods exhibit optimal convergence and computational complexity properties and are suitable for parallel implementation.We illustrate the efficiency of the proposed methods by various numerical experiments, including parallel results for large scale three dimensional problems.
|
|
| 4. |
|
|
| 5. |
- Fehn, Niklas, et al.
(author)
-
Numerical evidence of anomalous energy dissipation in incompressible Euler flows : towards grid-converged results for the inviscid Taylor-Green problem
- 2021
-
In: Journal of Fluid Mechanics. - : Cambridge University Press. - 0022-1120 .- 1469-7645. ; 932
-
Journal article (peer-reviewed)abstract
- The well-known energy dissipation anomaly in the inviscid limit, related to velocity singularities according to Onsager, still needs to be demonstrated by numerical experiments. The present work contributes to this topic through high-resolution numerical simulations of the inviscid three-dimensional Taylor-Green vortex problem using a novel high-order discontinuous Galerkin discretisation approach for the incompressible Euler equations. The main methodological ingredient is the use of a discretisation scheme with inbuilt dissipation mechanisms, as opposed to discretely energy-conserving schemes, which - by construction - rule out the occurrence of anomalous dissipation. We investigate effective spatial resolution up to 8192(3) (defined based on the 2 pi-periodic box) and make the interesting phenomenological observation that the kinetic energy evolution does not tend towards exact energy conservation for increasing spatial resolution of the numerical scheme, but that the sequence of discrete solutions seemingly converges to a solution with non-zero kinetic energy dissipation rate. Taking the fine-resolution simulation as a reference, we measure grid-convergence with a relative L-2-error of 0.27% for the temporal evolution of the kinetic energy and 3.52% for the kinetic energy dissipation rate against the dissipative fine-resolution simulation. The present work raises the question of whether such results can be seen as a numerical confirmation of the famous energy dissipation anomaly. Due to the relation between anomalous energy dissipation and the occurrence of singularities for the incompressible Euler equations according to Onsager's conjecture, we elaborate on an indirect approach for the identification of finite-time singularities that relies on energy arguments.
|
|
| 6. |
- Ge, Zhouyang, et al.
(author)
-
Effective slip over partially filled microcavities and its possible failure
- 2018
-
In: Physical Review Fluids. - : American Physical Society. - 2469-990X. ; 3:5
-
Journal article (peer-reviewed)abstract
- Motivated by the emerging applications of liquid-infused surfaces (LIS), we study the drag reduction and robustness of transverse flows over two-dimensional microcavities partially filled with an oily lubricant. Using separate simulations at different scales, characteristic contact line velocities at the fluid-solid intersection are first extracted from nanoscale phase field simulations and then applied to micronscale two-phase flows, thus introducing a multiscale numerical framework to model the interface displacement and deformation within the cavities. As we explore the various effects of the lubncant-toouter-fluid viscosity ratio A2/A0 th(mu)over tilde( )c(mu)over tilde(1), thary number Ca, the static contact angle A> and t theta(s), filling fraction of the cavity <5, we f delta d that the effective slip is most sensitive to the parameter S. The effects of A2/A1 an(mu)over tilde( )A(mu)over tilde(a )re ge theta(s)erally intertwined but weakened if <5 < 1. delta M 1er, for an initial filling fraction S = 0.94 delta our results show that the effective slip is nearly independent of the capillary number when it is small. Further increasing Ca to about O.OIA1/A20.01(mu)over tilde(1)/(mu)over tilde(2)ntify a possible failure mode, associated with lubricants draining from the LIS, for A2/A1 A (mu)over tilde(2)1(mu)over tilde(1)V less than or similar to y viscous lubricants (e.g., A2/A1 > (mu)over tilde()),(mu)over tilde(h)owever, are immune to such failure due to their generally larger contact line velocity.
|
|
| 7. |
|
|
| 8. |
- Ge, Zhouyang, et al.
(author)
-
Effective slip over partially filled microcavities and its possible failure
- 2018
-
In: Physical Review Fluids. - : APS. - 2469-990X. ; 3:5
-
Journal article (peer-reviewed)abstract
- Motivated by the emerging applications of liquid-infused surfaces (LIS), we study the drag reduction and robustness of transverse flows over two-dimensional microcavities partially filled with an oily lubricant. Using separate simulations at different scales, characteristic contact line velocities at the fluid-solid intersection are first extracted from nanoscale phase field simulations and then applied to micronscale two-phase flows, thus introducing a multiscale numerical framework to model the interface displacement and deformation within the cavities. As we explore the various effects of the lubricant-to-outer-fluid viscosity ratio ˜?2/˜?1, the capillary number Ca, the static contact angle ??, and the filling fraction of the cavity ?, we find that the effective slip is most sensitive to the parameter ?. The effects of ˜?2/˜?1 and ?? are generally intertwined but weakened if ?<1. Moreover, for an initial filling fraction ?=0.94, our results show that the effective slip is nearly independent of the capillary number when it is small. Further increasing Ca to about 0.01˜?1/˜?2, we identify a possible failure mode, associated with lubricants draining from the LIS, for ˜?2/˜?1≲0.1. Very viscous lubricants (e.g., ˜?2/˜?1>1), however, are immune to such failure due to their generally larger contact line velocity.
|
|
| 9. |
- Golshan, Shahab, et al.
(author)
-
Lethe-DEM : an open-source parallel discrete element solver with load balancing
- 2023
-
In: COMPUTATIONAL PARTICLE MECHANICS. - : Springer Nature. - 2196-4378 .- 2196-4386. ; 10:1, s. 77-96
-
Journal article (peer-reviewed)abstract
- Approximately 75% of the raw material and 50% of the products in the chemical industry are granular materials. The discrete element method (DEM) provides detailed insights of phenomena at particle scale, and it is therefore often used for modeling granular materials. However, because DEM tracks the motion and contact of individual particles separately, its computational cost increases nonlinearly O (n(p) log(n(p))) - O (n(2)) (depending on the algorithm) with the number of particles (n(p)). In this article, we introduce a new open-source parallel DEM software with load balancing: Lethe-DEM. Lethe-DEM, a module of Lethe, consists of solvers for two-dimensional and three-dimensional DEM simulations. Load balancing allows LetheDEM to significantly increase the parallel efficiency by approximate to 25-70% depending on the granular simulation. We explain the fundamental modules of Lethe-DEM, its software architecture, and the governing equations. Furthermore, we verify LetheDEM with several tests including analytical solutions and comparison with other software. Comparisons with experiments in a flat-bottomed silo, wedge-shaped silo, and rotating drum validate Lethe-DEM. We investigate the strong and weak scaling of Lethe-DEM with 1 <= n(c) <= 192 and 32 <= n(c) <= 320 processes, respectively, with and without load balancing. The strong-scaling analysis is performed on the wedge-shaped silo and rotating drum simulations, while for the weak-scaling analysis, we use a dam-break simulation. The best scalability of Lethe-DEM is obtained in the range of 5000 <= n(p)/n(c) <= 15,000. Finally, we demonstrate that large-scale simulations can be carried out with Lethe-DEM using the simulation of a three-dimensional cylindrical silo with n(p) = 4.3 x 10(6) on 320 cores.
|
|
| 10. |
|
|
