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Practical Kinetic Models for Dense Fluids
Ilya Karlin, Seyed Ali Hosseini
https://arxiv.org/abs/2508.00577 https://arxiv.org/pdf/2508.00577

Practical Kinetic Models for Dense Fluids
Nonlinear idempotent operator instead of a linear projection is introduced to derive kinetic models for dense fluids. A new lattice Boltzmann model for compressible two-phase flow is derived based on the Enskog--Vlasov kinetic equation as an example of practical importance.

Phase-Field Modeling of Two-Phase Flows: A Projection-Based Cahn-Hilliard-Navier-Stokes Framework
Sukriti Manna, Constantine M Megaridis, Subramanian KRS Sankaranarayanan
https://arxiv.org/abs/2509.00082

Phase-Field Modeling of Two-Phase Flows: A Projection-Based Cahn-Hilliard-Navier-Stokes Framework
The coupled Cahn-Hilliard and Navier-Stokes (CH-NS) equations provide a powerful framework for modeling multiphase flows with diffuse interfaces, enabling simulations of droplet breakup, bubble dynamics, and hydrodynamic instabilities. These capabilities are vital in boiling heat transfer, microfluidics, coating, additive manufacturing, and oil-water separation, where resolving fluid-fluid interactions is essential. Numerically, the CH-NS system is challenging: the Cahn-Hilliard equation involv…

Fractal Dimension in Nonlinear Wave Dynamics Governed by a Nonlinear Partial Differential Equation
Saugata Dutta, Kajal Kumar Mondal, Prasanta Chatterjee
https://arxiv.org/abs/2508.01816

Fractal Dimension in Nonlinear Wave Dynamics Governed by a Nonlinear Partial Differential Equation
This work presents a detailed analytical and geometrical investigation of the (2+1)-dimensional Boiti-Leon-Pempinelli system, a nonlinear dispersive model arising in the context of fluid and plasma dynamics. By employing a projective Riccati-based ansatz, a new class of exact solutions is systematically derived. These solutions, when visualized, exhibit intricate geometrical features that evolve across multiple spatial scales. To quantify this complexity, a voxel-based box-counting dimension an…

Projection-Based Solver for Viscoelastic Stokes Flow using FFTs
Georg Rempfer, Chengkai Zhu, Bart Stam, Mae Nesenberend, Debabrata Panja, Joost de Graaf
https://arxiv.org/abs/2509.01327

Projection-Based Solver for Viscoelastic Stokes Flow using FFTs
Understanding the flow of complex media is relevant for a wide range of research fields and industrial applications. Several numerical approaches exist by which approximate solutions can be determined for the Stokes equations that describe microhydrodynamic flows at the continuum level. However, achieving efficiency and accuracy for an incompressible fluid remains challenging. Here, we present an algorithm for solving the Stokes equations for an Oldroyd-B fluid using Fourier transforms. We gain…

$\textit{A Priori}$ Error Analysis for the $p$-Stokes Equations with Slip Boundary Conditions: A Discrete Leray Projection Framework
Alex Kaltenbach, J\"orn Wichmann
https://arxiv.org/abs/2507.15016

$\textit{A Priori}$ Error Analysis for the $p$-Stokes Equations with Slip Boundary Conditions: A Discrete Leray Projection Framework
We present an $\textit{a priori}$ error analysis for the kinematic pressure in a fully-discrete finite-differences/-elements discretization of the unsteady $p$-Stokes equations, modelling non-Newtonian fluids. This system is subject to both impermeability and perfect Navier slip boundary conditions, which are incorporated either weakly via Lagrange multipliers or strongly in the discrete velocity space. A central aspect of the $\textit{a priori}$ error analysis is the discrete Leray projection,…

Numerical investigations around the Gallavotti-Cohen Fluctuation Theorem on Log-lattices
Guillaume Costa (CEA), B\'ereng\`ere Dubrulle (CEA)
https://arxiv.org/abs/2508.17943

Numerical investigations around the Gallavotti-Cohen Fluctuation Theorem on Log-lattices
Using the recent concept of fluids projected onto Log-Lattices, we investigate the validity of the Gallavotti-Cohen Fluctuation Theorem (GCFT) in the context of fluid mechanics. The dynamics of viscous flows are inherently irreversible, which violates a fundamental assumption of the fluctuation theorem. To address this issue, Gallavotti introduced a new model, the Reversible Navier-Stokes Equation (RNS), which recovers the time-reversal symmetry of the Navier-Stokes (NS) equations while retaini…

Higher-Oder Splitting Schemes for Fluids with Variable Viscosity
Richard Schussnig, Niklas Fehn, Douglas Ramalho Queiroz Pacheco, Martin Kronbichler
https://arxiv.org/abs/2506.14424

Higher-Oder Splitting Schemes for Fluids with Variable Viscosity
This article investigates matrix-free higher-order discontinuous Galerkin (DG) discretizations of the Navier-Stokes equations for incompressible flows with variable viscosity. The viscosity field may be prescribed analytically or governed by a rheological law, as often found in biomedical or industrial applications. We compare several linearized variants of saddle point block systems and projection-based splitting time integration schemes in terms of their computational performance. Compared to…

Flow-dependent tagging of $^{214}$Pb decays in the LZ dark matter detector
J. Aalbers, D. S. Akerib, A. K. Al Musalhi, F. Alder, C. S. Amarasinghe, A. Ames, T. J. Anderson, N. Angelides, H. M. Ara\'ujo, J. E. Armstrong, M. Arthurs, A. Baker, S. Balashov, J. Bang, J. W. Bargemann, E. E. Barillier, K. Beattie, T. Benson, A. Bhatti, T. P. Biesiadzinski, H. J. Birch, E. Bishop, G. M. Blockinger, B. Boxer, C. A. J. Brew, P. Br\'as, S. Burdin, M. C. Carmona-Benitez, M. Carter, A. Cha…

Flow-dependent tagging of $^{214}$Pb decays in the LZ dark matter detector
The LUX-ZEPLIN (LZ) experiment is searching for dark matter interactions in a liquid xenon time projection chamber (LXe-TPC). This article demonstrates how control of the flow state in the LXe-TPC enables the identification of pairs of sequential alpha-decays, which are used to map fluid flow and ion drift in the liquid target. The resulting transport model is used to tag $^{214}$Pb beta-decays, a leading background to dark matter signals in LZ. Temporally evolving volume selections, at a cost …

The inverse initial data problem for anisotropic Navier-Stokes equations via Legendre time reduction method
Cong B. Van, Thuy T. Le, Loc H. Nguyen
https://arxiv.org/abs/2507.16810

The inverse initial data problem for anisotropic Navier-Stokes equations via Legendre time reduction method
We consider the inverse initial data problem for the compressible anisotropic Navier-Stokes equations, where the goal is to reconstruct the initial velocity field from lateral boundary observations. This problem arises in applications where direct measurements of internal fluid states are unavailable. We introduce a novel computational framework based on Legendre time reduction, which projects the velocity field onto an exponentially weighted Legendre basis in time. This transformation reduces …