arXiv subjects

Stephan B. Lunowa

Publications and source records attributed to Stephan B. Lunowa.

6 recordsLinked to original sources

arXiv2026

An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow

We establish the equivalence between a classical moment closure and a nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow in the linearized Hookean spring chain setting. The variational formulation is based on the Dirac-Frankel principle applied to a Gaussian approximation manifold endowed with the Fisher-Rao information metric. We show that the invariance of this manifold under the linear configurational dynamics yields an exact evolution for the macroscopic conformation tensor, recovering the classical diffusive Oldroyd-B closure. While the equivalence only holds in the linearized setting, the associated variational framework provides an abstract error representation. Thus it can serve in future work as a starting point for the systematic construction of reduced approximation schemes for polymeric flows with nonlinear forcing laws.

math.SP↗

arXiv2026

Effective permeabilities for flow through anisotropic microscopic geometries

This work develops a computational and theoretical framework for determining effective permeabilities in anisotropic microscopic geometries containing dense, fibre-like obstacles, motivated by the need to model flow in coiled aneurysm domains accurately. Building on homogenisation theory and fully resolved simulations in Representative Elementary Volumes (REVs), we validate the permeability model introduced in [C. Boutin, Study of permeability by periodic and self-consistent homogenisation. Eur. J. Mech. A Solids, 19(4):603-632, 2000] and propose a systematic methodology for capturing the directional variations induced by fibre orientation. The resulting permeability tensors are incorporated into macroscopic flow simulations based on the Darcy equation, enabling direct comparison of anisotropic and isotropic permeability models across several benchmark configurations. Our findings show that anisotropy has a significant impact on local flow direction and magnitude, generating directional permeability contrasts which cannot be reproduced by classical isotropic approximations. By integrating coil-induced microstructural effects into continuum-scale hemodynamic models, the proposed approach enables more realistic assessment of post-treatment aneurysm flow behaviour. Beyond this clinical application, the framework is broadly applicable to other biomedical and engineering systems involving fibrous or filamentous porous microstructures.

physics.flu-dyn↗

arXiv2026

A lattice Boltzmann method for Biot's consolidation model of linear poroelasticity

Biot's consolidation model is a classical model for the evolution of deformable porous media saturated by a fluid and has various interdisciplinary applications. While numerical solution methods to solve poroelasticity by typical schemes such as finite differences, finite volumes or finite elements have been intensely studied, lattice Boltzmann methods for poroelasticity have not been developed yet. In this work, we propose a novel semi-implicit coupling of lattice Boltzmann methods to solve Biot's consolidation model in two dimensions. To this end, we use a single-relaxation-time lattice Boltzmann method for reaction-diffusion equations to solve the Darcy flow and combine it with a recent pseudo-time multi-relaxation-time lattice Boltzmann scheme for quasi-static linear elasticity. We employ a multi-grid method for the latter scheme to achieve quasi-optimal computational cost. For the coupling between the equations, we develop a centered update scheme, that incorporates both explicit and semi-implicit contributions. The numerical results demonstrate that naive (explicit or semi-implicit) coupling schemes lead to instabilities when the poroelastic system is strongly coupled. However, the newly developed centered coupling scheme is stable and accurate in all considered cases, even for the Biot--Willis coefficient being one. Furthermore, the numerical results for Terzaghi's consolidation problem and a two-dimensional extension thereof highlight that the scheme is even able to capture discontinuous solutions arising from instantaneous loading.

math.NA↗

arXiv2024

On the Convergence of Learning Algorithms in Bayesian Auction Games

Equilibrium problems in Bayesian auction games can be described as systems of differential equations. Depending on the model assumptions, these equations might be such that we do not have a rigorous mathematical solution theory. The lack of analytical or numerical techniques with guaranteed convergence for the equilibrium problem has plagued the field and limited equilibrium analysis to rather simple auction models such as single-object auctions. Recent advances in equilibrium learning led to algorithms that find equilibrium under a wide variety of model assumptions. We analyze first- and second-price auctions where simple learning algorithms converge to an equilibrium. The equilibrium problem in auctions is equivalent to solving an infinite-dimensional variational inequality (VI). Monotonicity and the Minty condition are the central sufficient conditions for learning algorithms to converge to an equilibrium in such VIs. We show that neither monotonicity nor pseudo- or quasi-monotonicity holds for the respective VIs. The second-price auction's equilibrium is a Minty-type solution, but the first-price auction is not. However, the Bayes--Nash equilibrium is the unique solution to the VI within the class of uniformly increasing bid functions, which ensures that gradient-based algorithms attain the equilibrium in case of convergence, as also observed in numerical experiments.

cs.GT↗

arXiv2024

Numerical simulation of dilute polymeric fluids with memory effects in the turbulent flow regime

We address the numerical challenge of solving the Hookean-type time-fractional Navier--Stokes--Fokker--Planck equation, a history-dependent system of PDEs defined on the Cartesian product of two $d$-dimensional spaces in the turbulent regime. Due to its high dimensionality, the non-locality with respect to time, and the resolution required to resolve turbulent flow, this problem is highly demanding. To overcome these challenges, we employ the Hermite spectral method for the configuration space of the Fokker--Planck equation, reducing the problem to a purely macroscopic model. Considering scenarios for available analytical solutions, we prove the existence of an optimal choice of the Hermite scaling parameter. With this choice, the macroscopic system is equivalent to solving the coupled micro-macro system. We apply second-order time integration and extrapolation of the coupling terms, achieving, for the first time, convergence rates for the fully coupled time-fractional system independent of the order of the time-fractional derivative. Our efficient implementation of the numerical scheme allows turbulent simulations of dilute polymeric fluids with memory effects in two and three dimensions. Numerical simulations show that memory effects weaken the drag-reducing effect of added polymer molecules in the turbulent flow regime.

math.NA↗

arXiv2024

A Lattice Boltzmann Method for Non-Newtonian Blood Flow in Coiled Intracranial Aneurysms

Intracranial aneurysms are the leading cause of hemorrhagic stroke. One of the established treatment approaches is the embolization induced by coil insertion. However, the prediction of treatment and subsequent changed flow characteristics in the aneurysm is still an open problem. In this work, we present an approach based on a patient-specific geometry and parameters including a coil representation as inhomogeneous porous medium. The model consists of the volume-averaged Navier-Stokes equations for a non-Newtonian blood rheology. We solve these equations using a problem-adapted lattice Boltzmann method and present a comparison between fully-resolved and volume-averaged simulations. The results indicate the validity of the model. Overall, this workflow allows for patient specific assessment of the flow due to potential treatment.

math.NA↗