A block-coupled Finite Volume methodology for linear elasticity and unstructured meshes

Cardiff, Philip; Tuković, Željko; Jasak, Hrvoje; Ivanković, Alojz

doi:10.1016/j.compstruc.2016.07.004

Cited by 69 publications

(68 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The implementation of the finite area method has been used and verified for several problems [38,59,60,35,61], as well as the related finite volume method (e.g., [57]) and the interpolation scheme [52]. In this work, we will present four examples with increasing complexity, focusing on different aspects.…”

Section: Resultsmentioning

confidence: 99%

A finite area scheme for shallow granular flows on three-dimensional surfaces

Rauter

Tuković

2018

Computers & Fluids

Self Cite

View full text Add to dashboard Cite

Shallow flow or thin liquid film models are used for a wide range of physical and engineering problems. They are applicable to free surface flows, when the flow thickness is distinctly smaller than the lateral dimension. Respective situations exist in automotive and aircraft engineering (soiling, icing, exterior water management), industrial processes (coating, fire suppression), environmental flows (river and lake hydrodynamics, atmospheric flows), and natural hazards (floods, avalanches, debris flow). Shallow flow models allow capturing the free surface of the fluid with little effort and reducing the three-dimensional problem to a quasi two-dimensional problem through depth-integrating the flow fields. Despite remarkable progress of such models in the last decade, accurate description of complex topography remains a challenge. Interaction with topography is particularly critical for granular flows, because their rheology requires modeling of the pressure field, which is strongly linked to surface curvature and associated centrifugal forces. Shallow granular flow models are usually set up in surface-aligned curvilinear coordinates, and velocity is represented as a two-dimensional surfacealigned vector field. The transformation from Cartesian to curvilinear coordinates introduces fictitious forces, however, which result in complex governing equations. In this paper, we set up the shallow flow model in three-dimensional Cartesian coordinates and preserve three-dimensional velocity in the depthintegrated model. Topography is taken into account with a constraint on velocity. This approach is commonly applied by the thin liquid film community. The advantage is a curvature-free mathematical description that is convenient for complex topographies. The constraint on velocity yields a solution for the pressure field, which is required for the pressure-dependent rheology of granular materials. The model is therefore well-suited for granular flows on three-dimensional terrain, e.g., avalanches. The mathematical model is solved with a second-order accurate, implicit finite area scheme, based on the open source software OpenFOAM. We conduct numerical simulations for various cases to verify the numerical routine based on comparisons with analytical results and a grid refinement study. We establish connections to former solutions and discuss advantages and drawbacks of the proposed method from both mechanical and numerical perspectives.

show abstract

Section: Resultsmentioning

confidence: 99%

A finite area scheme for shallow granular flows on three-dimensional surfaces

Rauter

Tuković

2018

Computers & Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…In particular, by building on a discontinuous Galerkin-like structure, they are explicitly formulated to handle discontinuities and anisotropic material properties such as typically encountered in geological applications. In contrast, existing cell-centered finite volume discretizations typically rely on either face values of material properties (see, e.g., the recent paper [22] and the references therein) or smooth interpolations of the displacement field [23,24]. While the latter approach has recently been extended to handle layered media [25], geological media are often considered to be everywhere heterogeneous, requiring methods that adapt to more complex material structures.…”

mentioning

confidence: 99%

Finite volume methods for elasticity with weak symmetry

Keilegavlen

Nordbotten

2017

Numerical Meth Engineering

View full text Add to dashboard Cite

We introduce a new cell-centered finite volume discretization for elasticity with weakly enforced symmetry of the stress tensor. The method is motivated by the need for robust discretization methods for deformation and flow in porous media and falls in the category of multi-point stress approximations (MPSAs). By enforcing symmetry weakly, the resulting method has flexibility beyond previous MPSA methods. This allows for a construction of a method that is applicable to simplexes, quadrilaterals, and most planar-faced polyhedral grids in both 2D and 3D, and in particular, the method amends a convergence failure in previous MPSA methods for certain simplex grids. We prove convergence of the new method for a wide range of problems, with conditions that can be verified at the time of discretization. We present the first set of comprehensive numerical tests for the MPSA methods in three dimensions, covering Cartesian and simplex grids, with both heterogeneous and nearly incompressible media. The tests show that the new method consistently is second order convergent in displacement, despite being the lowest order, with a rate that mostly is between 1 and 2 for stresses. The results further show that the new method is more robust and computationally cheaper than previous MPSA methods.

show abstract

“…Similar to the methods in [40,41], the gradient of the displacement (and hence, the strain and stress tensors) are evaluated directly on the cell face centers. To do so, the gradient is decomposed into the normal and the tangential derivatives and a specific numerical scheme is used for each term.…”

Section: Solid Solvermentioning

confidence: 99%

A scalable framework for the partitioned solution of fluid–structure interaction problems

et al. 2020

View full text Add to dashboard Cite

In this work, we present a scalable and efficient parallel solver for the partitioned solution of fluid-structure interaction problems through multi-code coupling. Two instances of an in-house parallel software, Ter-moFluids, are used to solve the fluid and the structural sub-problems, coupled together on the interface via the preCICE coupling library. For fluid flow, the Arbitrary Lagrangian-Eulerian form of the Navier-Stokes equations is solved on an unstructured conforming grid using a second-order finitevolume discretization. A parallel dynamic mesh method for unstructured meshes is used to track the moving boundary. For the structural problem, the nonlinear elastodynamics equations are solved on an unstructured grid using a second-order finite-volume method. A semi-implicit FSI coupling method is used which segregates the fluid pressure term and couples it strongly to the structure, while the remaining fluid terms and the geometrical nonlinearities are only loosely coupled. A robust and advanced multivector quasi-Newton method is used for the coupling iterations between the solvers. Both the fluid and the structural solver use distributed-memory parallelism. The intra-solver communication required for data update in the solution process is carried out using non-blocking point-to-point communicators. The inter-code communication is fully parallel and point-to-point, avoiding any central communication unit. Inside each single-physics solver, the load is balanced by dividing the computational domain into fairly equal blocks for each process. Additionally, a load balancing model is used at the inter-code level to minimize the overall idle time of the processes. Two strating the accuracy and computational efficiency of the coupled solver. Strong scalability test results show a parallel efficiency of 83% on 10,080 CPU cores.

show abstract

A block-coupled Finite Volume methodology for linear elasticity and unstructured meshes

Cited by 69 publications

References 33 publications

A finite area scheme for shallow granular flows on three-dimensional surfaces

A finite area scheme for shallow granular flows on three-dimensional surfaces

Finite volume methods for elasticity with weak symmetry

A scalable framework for the partitioned solution of fluid–structure interaction problems

Contact Info

Product

Resources

About