Related papers: Wave-Appropriate Reconstruction of Compressible Mu…
The exhaustive classification of stationary incompressible flows with constant total pressure of ideal infinitely electrically conducting fluid is given. By introduction of curvilinear coordinates based on streamlines and magnetic lines of…
We investigate the qualitative dynamics of smooth solutions to the radially symmetric isentropic compressible Euler equations, focusing specifically on the evolution of rarefactive and compressive wave characters across three distinct…
In this article we present a novel staggered semi-implicit hybrid finite-volume/finite-element (FV/FE) method for the resolution of weakly compressible flows in two and three space dimensions. The pressure-based methodology introduced in…
In this paper, we present a unified nonequilibrium model of continuum mechanics for compressible multiphase flows. The model, which is formulated within the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC) equations,…
We present a novel pressure-based method for weakly compressible multiphase flows, based on a non-equilibrium Baer and Nunziato-type model. In this work, we describe the hyperbolic operator, thus we do not consider relaxation terms. The…
This paper concerns closed hypersurfaces of dimension $n(\geq 2)$ in the hyperbolic space ${\mathbb{H}}_{\kappa}^{n+1}$ of constant sectional curvature $\kappa$ evolving in direction of its normal vector, where the speed is given by a power…
A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier--Stokes equations. The approach linearizes convection using an extrapolated (Oseen-type) convecting velocity, producing a…
Compressible flow varies from ideal-gas behavior at high pressures where molecular interactions become important. Density is described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and…
Most learning-based image compression methods lack efficiency for high image quality due to their non-invertible design. The decoding function of the frequently applied compressive autoencoder architecture is only an approximated inverse of…
Volume-preserving hyperelastic materials are widely used to model near-incompressible materials such as rubber and soft tissues. However, the numerical simulation of volume-preserving hyperelastic materials is notoriously challenging within…
In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a…
Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…
The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with…
This paper considers large-scale simulations of wave propagation phenomena. We argue that it is possible to accurately compute a wavefield by decomposing it onto a largely incomplete set of eigenfunctions of the Helmholtz operator, chosen…
We study the long-time dynamics of small-amplitude solutions to the three-dimensional gravity-capillary water waves equations for an inviscid and irrotational fluid with periodic boundary conditions. We prove that, for almost all values of…
We derive a new formulation of the compressible Euler equations exhibiting remarkable structures, including surprisingly good null structures. The new formulation comprises covariant wave equations for the Cartesian components of the…
We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…
We introduce a second-order, central-upwind finite volume method for the discretization of nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. The semi-discrete version of the proposed method is based on a technique…
Following Brown[1], we construct composite operators for the scalar $\phi^3$ theory in six dimensions using renormalisation group methods with dimensional regularisation. We express bare scalar operators in terms of renormalised composite…
An energetically balanced, implicit integrator for non-hydrostatic vertical atmospheric dynamics on the sphere is presented. The integrator allows for the exact balance of energy exchanges in space and time for vertical atmospheric motions…