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1. Conservative unconditionally stable decoupled numerical schemes for the Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq system

   https://doi.org/10.1002/num.22841  

   Chen, Wenbin; Han, Daozhi; Wang, Xiaoming; Zhang, Yichao (September 2021, Numerical Methods for Partial Differential Equations)

   Abstract We propose two mass and heat energy conservative, unconditionally stable, decoupled numerical algorithms for solving the Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq system that models thermal convection of two‐phase flows in superposed free flow and porous media. The schemes totally decouple the computation of the Cahn–Hilliard equation, the Darcy equations, the heat equation, the Navier–Stokes equations at each time step, and thus significantly reducing the computational cost. We rigorously show that the schemes are conservative and energy‐law preserving. Numerical results are presented to demonstrate the accuracy and stability of the algorithms. 

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2. Fully decoupled energy-stable numerical schemes for two-phase coupled porous media and free flow with different densities and viscosities

   https://doi.org/10.1051/m2an/2023012  

   Gao, Yali; He, Xiaoming; Lin, Tao; Lin, Yanping (May 2023, ESAIM: Mathematical Modelling and Numerical Analysis)

   In this article, we consider a phase field model with different densities and viscosities for the coupled two-phase porous media flow and two-phase free flow, as well as the corresponding numerical simulation. This model consists of three parts: a Cahn–Hilliard–Darcy system with different densities/viscosities describing the porous media flow in matrix, a Cahn–Hilliard–Navier–Stokes system with different densities/viscosities describing the free fluid in conduit, and seven interface conditions coupling the flows in the matrix and the conduit. Based on the separate Cahn–Hilliard equations in the porous media region and the free flow region, a weak formulation is proposed to incorporate the two-phase systems of the two regions and the seven interface conditions between them, and the corresponding energy law is proved for the model. A fully decoupled numerical scheme, including the novel decoupling of the Cahn–Hilliard equations through the four phase interface conditions, is developed to solve this coupled nonlinear phase field model. An energy-law preservation is analyzed for the temporal semi-discretization scheme. Furthermore, a fully discretized Galerkin finite element method is proposed. Six numerical examples are provided to demonstrate the accuracy, discrete energy law, and applicability of the proposed fully decoupled scheme. 

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3. Global well-posedness of the velocity–vorticity-Voigt model of the 3D Navier–Stokes equations

   https://doi.org/https://doi.org/10.1016/j.jde.2018.08.033  

   Larios, A; Pei, Y; Rebholz, L (February 2019, Journal of differential equations)

   The velocity–vorticity formulation of the 3D Navier–Stokes equations was recently found to give excellent numerical results for flows with strong rotation. In this work, we propose a new regularization of the 3D Navier–Stokes equations, which we call the 3D velocity–vorticity-Voigt (VVV) model, with a Voigt regularization term added to momentum equation in velocity–vorticity form, but with no regularizing term in the vorticity equation. We prove global well-posedness and regularity of this model under periodic boundary conditions. We prove convergence of the model's velocity and vorticity to their counterparts in the 3D Navier–Stokes equations as the Voigt modeling parameter tends to zero. We prove that the curl of the model's velocity converges to the model vorticity (which is solved for directly), as the Voigt modeling parameter tends to zero. Finally, we provide a criterion for finite-time blow-up of the 3D Navier–Stokes equations based on this inviscid regularization. 

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4. Giant chiral magnetoelectric oscillations in a van der Waals multiferroic

   https://doi.org/10.1038/s41586-024-07678-5  

   Gao, Frank Y; Peng, Xinyue; Cheng, Xinle; Viñas_Boström, Emil; Kim, Dong Seob; Jain, Ravish K; Vishnu, Deepak; Raju, Kalaivanan; Sankar, Raman; Lee, Shang-Fan; et al (August 2024, Nature)

   Abstract Helical spin structures are expressions of magnetically induced chirality, entangling the dipolar and magnetic orders in materials^1–4. The recent discovery of helical van der Waals multiferroics down to the ultrathin limit raises prospects of large chiral magnetoelectric correlations in two dimensions^5,6. However, the exact nature and magnitude of these couplings have remained unknown so far. Here we perform a precision measurement of the dynamical magnetoelectric coupling for an enantiopure domain in an exfoliated van der Waals multiferroic. We evaluate this interaction in resonance with a collective electromagnon mode, capturing the impact of its oscillations on the dipolar and magnetic orders of the material with a suite of ultrafast optical probes. Our data show a giant natural optical activity at terahertz frequencies, characterized by quadrature modulations between the electric polarization and magnetization components. First-principles calculations further show that these chiral couplings originate from the synergy between the non-collinear spin texture and relativistic spin–orbit interactions, resulting in substantial enhancements over lattice-mediated effects. Our findings highlight the potential for intertwined orders to enable unique functionalities in the two-dimensional limit and pave the way for the development of van der Waals magnetoelectric devices operating at terahertz speeds. 

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5. Implementation of the Accurate Conservative Phase Field Method for two-phase incompressible flows in a finite volume framework, Proc. of the 9th Int. and 49th National Conf. on Fluid Mechanics and Fluid Power (FMFP), December 14-16, 2022, IIT Roorkee, Roorkee-247667, Uttarakhand, India. FMFP2022–1300.

   Jain, S.; Tafti, D. K. (December 2022, Proc. of the 9th Int. and 49th National Conf. on Fluid Mechanics and Fluid Power (FMFP))

   The phase field method provides a simple mass conserving method for solving two-phase immiscible - incompressible Navier-Stokes Equations. The relative ease in implementing this method compared to other interface reconstruction methods, coupled with its conservativeness and boundedness makes it an attractive alternative. We implement the method in a parallel structured multi-block generalized coordinate finite volume solver using a collocated grid arrangement within the framework of the fractional-step method. The discretization uses a second-order central difference method for both the Navier-Stokes and the phase field equations. A TVD-based averaging technique is used for calculating density at cell faces in the pressure correction step to handle high-density ratios. The simulation framework is verified in standard test cases: Zalesak Disk, a droplet in shear flow, Solitary Wave Runup, Rayleigh Taylor Instability, and the Dam Break Problem. A second-order rate of convergence and excellent phase volume conservation is observed. 

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