Related papers: Truly multi-dimensional all-speed methods for the …
Finite volume schemes often have difficulties to resolve the low Mach number (incompressible) limit of the Euler equations. Incompressibility is only non-trivial in multiple spatial dimensions. Low Mach fixes, however generally are applied…
This paper presents a new strategy to deal with the excessive diffusion that standard finite volume methods for compressible Euler equations display in the limit of low Mach number. The strategy can be understood as using centered…
A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and…
The Active Flux method is a finite volume method for hyperbolic conservation laws that uses both cell averages and point values as degrees of freedom. Several versions of such methods are currently under development. We focus on third order…
A new framework based on Boltzmann equation which is genuinely multidimensional and mesh-less is developed for solving Euler's equations. The idea is to use the method of moment of Boltzmann equation to operate in multidimensions using…
Hodograph equations for the n-dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Euler in implicit form and information on existence or absence…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
Active Flux is an extension of the Finite Volume method and additionally incorporates point values located at cell boundaries. This gives rise to a globally continuous approximation of the solution. Originally, the Active Flux method…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…
We consider numerical methods for linear parabolic equations in one spatial dimension having piecewise constant diffusion coefficients defined by a one parameter family of interface conditions at the discontinuity. We construct immersed…
Hodograph equations for the Euler equation in curved spaces with constant pressure are discussed. It is shown that the use of known results concerning geodesics and associated integrals allows to construct several types of hodograph…
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle,…
We study the global wellposedness of pressure-less Eulerian dynamics in multi-dimensions, with radially symmetric data. Compared with the 1D system, a major difference in multi-dimensional Eulerian dynamics is the presence of the spectral…
In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…
In this article, we report the equilibrium and nonequilibrium features of two-dimensional (2D) and three-dimensional (3D) Euler turbulence. To obtain a full range of equilibrium spectra, we perform pseudo-spectral simulations of Euler…
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the…
In this paper, we study the control system associated with the incompressible 3D Euler system. We show that the velocity field and pressure of the fluid are exactly controllable in projections by the same finite-dimensional control.…
A new discrete-velocity model is presented to solve the three-dimensional Euler equations. The velocities in the model are of an adaptive nature---both the origin of the discrete-velocity space and the magnitudes of the discrete-velocities…