Related papers: Behavior of different numerical schemes for popula…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
We develop an asymptotic-preserving scheme to solve evolution problems containing stiff transport terms. This scheme is based to a micro-macro decomposition of the unknown, coupled with a stabilization procedure. The numerical method is…
In this paper, we develop a new mass conservative numerical scheme for the simulations of a class of fluid-structure interaction problems. We will use the immersed boundary method to model the fluid-structure interaction, while the fluid…
We introduce the Discrete Inverse Continuity Equation (DICE) method, a generative modeling approach that learns the evolution of a stochastic process from given sample populations at a finite number of time points. Models learned with DICE…
Convection-diffusion problems arise in the modelling of many physical processes. Their typical solutions exhibit boundary and/or interior layers. Despite the linear nature of the differential operator, these problems pose still-unanswered…
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…
A new energy and enstrophy conserving scheme is evaluated using a suite of test cases over the global spherical domain or bounded domains. The evaluation is organized around a set of pre-defined properties: accuracy of individual opeartors,…
We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms representing friction and gravity. While discontinuities in…
This paper deals with the construction of numerical stable solutions of random mean square Fisher-KPP models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
We consider partial differential equations (PDE) of drift-diffusion type in the unit interval, supplemented by either two conservation laws or by a conservation law and a further boundary condition. We treat two different cases: (i) uniform…
We study the numerical approximation of singularly perturbed convection-diffusion problems on one-dimensional pipe networks. In the vanishing diffusion limit, the number and type of boundary conditions and coupling conditions at network…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisotropy, and promising potentials for accommodating automated…
The effects induced by numerical schemes and mesh geometry on the solution of two-dimensional supersonic inviscid flows are investigated in the context of the compressible Euler equations. Five different finite-difference schemes are…
This paper establishes a structure-preserving numerical scheme for the Cahn--Hilliard equation with degenerate mobility. First, by applying a finite volume method with upwind numerical fluxes to the degenerate Cahn--Hilliard equation…
We consider a mechanical system with impact and n degrees of freedom, written in generalized coordinates. The system is not necessarily Lagrangian. The representative point of the system must remain inside a set of constraints K; the…
We present a systematic methodology to develop high order accurate numerical approaches for linear advection problems. These methods are based on evolving parts of the jet of the solution in time, and are thus called jet schemes. Through…