Related papers: Bound-Preserving WENO Schemes for Temple-class sys…

Many problems in electrical engineering or fluid mechanics can be modeled by parabolic-elliptic interface problems, where the domain for the exterior elliptic problem might be unbounded. A possibility to solve this class of problems…

We present a newly developed cosmological hydrodynamics code based on weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. WENO is a higher order accurate finite difference scheme designed for problems with…

A structure-preserving Finite Element Method (FEM) for the transport equation in one- and two-dimensional domains is presented. This Distributed Parameter System (DPS) has non-collocated boundary control and observation, and reveals a…

In the present paper, a fluid-particle coupling method is directly derived from the Navier-Stokes equations (NSE) by applying the concept of volume-filtering, yielding a physically consistent methodology to incorporate solid wall boundary…

Solutions to many partial differential equations satisfy certain bounds or constraints. For example, the density and pressure are positive for equations of fluid dynamics, and in the relativistic case the fluid velocity is upper bounded by…

The computation of multiphase flows presents a subtle energetic equilibrium between potential (i.e., surface) and kinetic energies. The use of traditional interface-capturing schemes provides no control over such a dynamic balance. In the…

The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of…

For gradient flows, the existing structure-preserving schemes are difficult to achieve arbitrary high-order accuracy in time while preserving maximum-principle (MBP) and energy dissipating simultaneously. In this paper, we develop a new…

For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy, including the Willmore and the Helfrich flows, we consider a numerical approach. In this study, we construct a structure-preserving…

The properties of constrained fluids have increasingly gained relevance for applications ranging from materials to biology. In this work, we propose a multiscale model using twin neural networks to investigate the properties of a fluid…

We design and analyse an energy stable, structure preserving, well-balanced and asymptotic preserving (AP) scheme for the barotropic Euler system with gravity in the anelastic limit. The key to energy stability is the introduction of…

In this paper we propose new Z-type nonlinear weights of the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme for hyperbolic conservation laws. Instead of employing the classical smoothness indicators for the…

This paper develops high-order accurate, well-balanced (WB), and positivity-preserving (PP) finite volume schemes for shallow water equations on adaptive moving structured meshes. The mesh movement poses new challenges in maintaining the WB…

Existing numerical models of the swash zone are relatively inflexible in dealing with sediment transport due to a high dependence of the deployed numerical schemes on empirical sediment transport relations. Moreover, these models are…

This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and…

In recent years, kinetic equations have been used to model many social phenomena. A key feature of these models is that transition rate kernels involve Dirac delta functions, which capture sudden, discontinuous state changes. Here, we study…

We develop structure-preserving finite volume schemes for the barotropic Euler equations in the low Mach number regime. Our primary focus lies in ensuring both the asymptotic-preserving (AP) property and the discrete entropy stability. We…

The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…

We propose a structure-preserving scheme for a hybrid model that couples the time-dependent Ginzburg-Landau (TDGL) equation of superconducting vortex dynamics and the nonlinear Bardeen-Cooper-Schrieffer (BCS) gap equation. This formulation…

When a fluid flows over a solid surface, it creates a thin boundary layer where the flow velocity is influenced by the surface through viscosity, and can transition from laminar to turbulent at sufficiently high speeds. Understanding and…