Related papers: A fully well-balanced hydrodynamic reconstruction
First-order hydrostatic reconstruction (HR) schemes for shallow water equations are highly diffusive whereas high-order schemes can produce entropy-violating solutions. Our goal is to develop a flux correction with maximum antidiffusive…
The precise simulation of turbulent flows holds immense significance across various scientific and engineering domains, including climate science, freshwater science, and energy-efficient manufacturing. Within the realm of simulating…
We consider a non-linear variant of the transport-diffusion osmosis model for solving a variety of imaging problems such as shadow/soft-light removal and compact data representation. The non-linear behaviour is encoded in terms of a general…
A novel interface reconstruction strategy for volume of fluid (VOF) methods is introduced that represents the liquid-gas interface as two planes that co-exist within a single computational cell. In comparison to the piecewise linear…
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large…
High order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite coarse meshes and with very few restrictions on the kind of cells employed in the…
Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…
The reconstruction of water wave elevation from bottom pressure measurements is an important issue for coastal applications, but corresponds to a difficult mathematical problem. In this paper we present the derivation of a method which…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
In this paper we carry out numerical analysis for a family of simplified gas transport models with hydrate formation and dissociation in subsurface, in equilibrium and non-equilibrium conditions. These models are adequate for simulation of…
Ground based long-range passive imaging systems often suffer from degraded image quality due to a turbulent atmosphere. While methods exist for removing such turbulent distortions, many are limited to static sequences which cannot be…
In some previous works, two of the authors have introduced a strategy to develop high-order numerical methods for systems of balance laws that preserve all the stationary solutions of the system. The key ingredient of these methods is a…
We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…
We consider in this work the numerical resolution of a 2D shallow water system with a Coriolis effect and bottom friction stresses on unstructured meshes by a new Finite Volume Characteristics (FVC) scheme, which has been introduced in the…
This paper describes a numerical scheme for multi-fluid hydrodynamics in the limit of small mass densities of the charged particles. The inertia of the charged particles can then be neglected, which makes it possible to write an evolution…
We consider the depth-integrated non-hydrostatic system derived by Yamazaki et al. An efficient formally second-order well-balanced hybrid finite volume finite difference numerical scheme is proposed. The scheme consists of a two-step…
We present a conservation formulation and a numerical algorithm for the reduced-gravity shallow-water equations on a beta plane, subjected to a constant wind forcing that leads to the formation of double-gyre circulation in a closed ocean…
The paper is devoted to the numerical solution of elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a…
The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonlinear PDE models presents theoretical and numerical challenges…