3D modeling of generalized Newtonian fluid flow with data assimilation using the least-squares finite element method

Averweg, Solveigh; Schwarz, Alexander; Schwarz, Carina; Schröder, Jörg

doi:10.1016/j.cma.2022.114668

Cited by 7 publications

(4 citation statements)

References 62 publications

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“…The linearized inner systems were resolved by PARDISO, a direct solver that makes utilizes LU matrix factorization to reduce the number of iterations necessary to reach the desired level of convergence. Therefore, fewer iterations are necessary [ 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ]. In interconnect architectures, this technique can be used to simulate and describe a variety of physical operations.…”

Section: Numerical Procedures and Code Validationmentioning

confidence: 99%

Assessment of heat transfer and the consequences of iron oxide (Fe3O4) nanoparticles on flow of blood in an abdominal aortic aneurysm

Hussain,

Riaz Dar,

Alrasheedi

et al. 2023

Heliyon

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Section: Numerical Procedures and Code Validationmentioning

confidence: 99%

Assessment of heat transfer and the consequences of iron oxide (Fe3O4) nanoparticles on flow of blood in an abdominal aortic aneurysm

Hussain,

Riaz Dar,

Alrasheedi

et al. 2023

Heliyon

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“…Due to the stronger patching condition compared to the H (div)-conforming Raviart-Thomas discretizations certain solutions cannot be approximated well using Q 1 elements; see, e.g., [60] for a detailled discussion. However, such discretizations have been considered also elsewhere, e.g., in the context of least-squares formulations [5], where no LBB condition has to be fulfilled; see also [56], where different combinations of Raviart-Thomas elements with Lagrange elements have been considered for least-squares formulations of the Navier-Stokes problem in the almost incompressible case. Considering coupled problems involving mechanics and diffusion, the hybridization technique introduced in [66] is promising, where the incompressibility constraint of the fluid is exactly enforced by altering the balance of solute volume (7) as a consequence of the constant volume of the solid, i.e.…”

Section: A3 Discretization Of the Fluid Fluxmentioning

confidence: 99%

Monolithic parallel overlapping Schwarz methods in fully-coupled nonlinear chemo-mechanics problems

et al. 2023

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We consider the swelling of hydrogels as an example of a chemo-mechanical problem with strong coupling between the mechanical balance relations and the mass diffusion. The problem is cast into a minimization formulation using a time-explicit approach for the dependency of the dissipation potential on the deformation and the swelling volume fraction to obtain symmetric matrices, which are typically better suited for iterative solvers. The MPI-parallel implementation uses the software libraries deal.II, p4est and FROSch (Fast of Robust Overlapping Schwarz). FROSch is part of the Trilinos library and is used in fully algebraic mode, i.e., the preconditioner is constructed from the monolithic system matrix without making explicit use of the problem structure. Strong and weak parallel scalability is studied using up to 512 cores, considering the standard GDSW (Generalized Dryja-Smith-Widlund) coarse space and the newer coarse space with reduced dimension. The FROSch solver is applicable to the coupled problems within in the range of processor cores considered here, although numerical scalablity cannot be expected (and is not observed) for the fully algebraic mode. In our strong scalability study, the average number of Krylov iterations per Newton iteration is higher by a factor of up to six compared to a linear elasticity problem. However, making mild use of the problem structure in the preconditioner, this number can be reduced to a factor of two and, importantly, also numerical scalability can then be achieved experimentally. Nevertheless, the fully algebraic mode is still preferable since a faster time to solution is achieved.

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“…The question of how to assimilate measured data into large-scale computations of flow problems is receiving increasing attention from the computational mathematics community [3,7,22,26,28,36]. There are several different situations where such data assimilation problems as can be seen in the above examples.…”

Section: Introductionmentioning

confidence: 99%

Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation

Burman,

Garg,

Preuss

2024

ESAIM: M2AN

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In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive quantitative local error estimates for the velocity, which account for noise level and polynomial degree, using the stability of the continuous problem in the form of a conditional stability estimate. Numerical examples illustrate the performances of the method with respect to the polynomial order and perturbations in the data. We observe that the higher order polynomials may be efficient for ill-posed problems, but are also more sensitive for problems with poor stability due to the ill-conditioning of the system.

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3D modeling of generalized Newtonian fluid flow with data assimilation using the least-squares finite element method

Cited by 7 publications

References 62 publications

Assessment of heat transfer and the consequences of iron oxide (Fe3O4) nanoparticles on flow of blood in an abdominal aortic aneurysm

Assessment of heat transfer and the consequences of iron oxide (Fe3O4) nanoparticles on flow of blood in an abdominal aortic aneurysm

Monolithic parallel overlapping Schwarz methods in fully-coupled nonlinear chemo-mechanics problems

Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation

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