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Semi-Lagrangian finite element exterior calculus for incompressible flows
We develop a semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions on arbitrary...
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Helically symmetric equilibria for some ideal and resistive MHD plasmas with incompressible flows
In this paper, the problem of finding exact solutions to the magnetohydrodynamic (MHD) equations in the presence of incompressible mass flows with...
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On parabolic instability regions for inviscid incompressible annular flows
We consider the azimuthal instability problem of inviscid incompressible swirling flows following the work of Fung (J Fluid Mech 127:83–90, 1983) and...
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Reynolds-BlendedWeights for BDDC in Applications to Incompressible Flows
We investigate the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to numerical solution of problems of...
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On the Dynamics of the Boundary Vorticity for Incompressible Viscous Flows
The dynamical equation of the boundary vorticity has been obtained, which shows that the viscosity at a solid wall is doubled as if the fluid became...
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A Semi-implicit Finite Volume Scheme for Incompressible Two-Phase Flows
This paper presents a mass and momentum conservative semi-implicit finite volume (FV) scheme for complex non-hydrostatic free surface flows,...
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Uniform Regularity Estimates for Three Dimensional Nonhomogeneous Incompressible Heat Conducting Navier–Stokes Flows
In this paper, we investigate the nonhomogeneous incompressible heat conducting Navier–Stokes flows in the three dimensional whole space. One...
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The well-posedness of incompressible rotational jet flows with gravity
This paper is concerned with the well-posedness theory and geometric property of steady two-dimensional incompressible jet flow with vorticity and...
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Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows
Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows, it is desirable to develop...
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A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions
Based on two-grid discretizations and quadratic equal-order finite elements for the velocity and pressure approximations, we develop a three-step...
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Large deviations for the interchange process on the interval and incompressible flows
We use the framework of permuton processes to show that large deviations of the interchange process are controlled by the Dirichlet energy. This...
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Interfaces in incompressible flows
The motion of both internal and surface waves in incompressible fluids under capillary and gravity forces is a major research topic. In particular,...
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High-Order Bound-Preserving Local Discontinuous Galerkin Methods for Incompressible and Immiscible Two-Phase Flows in Porous Media
In this paper, we develop high-order bound-preserving (BP) local discontinuous Galerkin methods for incompressible and immiscible two-phase flows in...
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A Fully-Decoupled Artificial Compressible Crank–Nicolson–Leapfrog Time Step** Scheme for the Phase Field Model of Two-Phase Incompressible Flows
In this paper, we consider efficient numerical approximations for the phase field model of two-phase incompressible flows. To develop...
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Error Analysis of a Unconditionally Stable BDF2 Finite Element Scheme for the Incompressible Flows with Variable Density
Based on an equivalent form of the variable density flows, we propose and study a second-order linearized finite element scheme for the approximation...
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Steady-State Flows of Ideal Incompressible Fluid with Velocity Pointwise Orthogonal to the Pressure Gradient
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations...
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Finding Steady Poiseuille-Type Flows for Incompressible Polymeric Fluids by the Relaxation Method
AbstractStabilization of flows of an incompressible viscoelastic polymeric fluid in a channel with a rectangular cross section under the action of a...
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Exact Solutions to the Navier–Stokes Equations and the Equation of Continuity for Twisted Axially Symmetric Flows of a Viscous Incompressible Fluid
We study exact solutions to the nonstationary Navier–Stokes equations and the equation of continuity for a special class of twisted axially symmetric...
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A Discrete Nine-Velocity Model of the Boltzmann Equation: Solution in the Form of Wild Sum and Applications to Simulating Incompressible Flows
AbstractA discrete kinetic nine-velocity model of the Boltzmann equation on a plane is considered. In the limit of small free path and low bulk...
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On a Navier–Stokes–Cahn–Hilliard system for viscous incompressible two-phase flows with chemotaxis, active transport and reaction
We analyze a Navier–Stokes–Cahn–Hilliard model for viscous incompressible two-phase flows where the mechanisms of chemotaxis, active transport and...