Related papers: A structure-preserving semi-implicit four-split sc…
In this paper, we develop a new free-stream preserving (FP) method for high-order upwind conservative finite-difference (FD) schemes on the curvilinear grids. This FP method is constrcuted by subtracting a reference cell-face flow state…
In this article, we propose a novel conservative diffuse-interface method for the simulation of immiscible compressible two-phase flows. The proposed method discretely conserves the mass of each phase, momentum and total energy of the…
Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…
In this paper, we investigate the correlated diffusion of two ion species governed by a Poisson-Nernst-Planck (PNP) system. Here we further validate the numerical scheme recently proposed in \cite{astuto2025asymptotic}, where a time…
Identifying governing partial differential equations (PDEs) from noisy spatiotemporal data remains challenging due to differentiation-induced noise amplification and ambiguity from overcomplete libraries. We propose a prior-informed…
A nonhydrostatic dynamical core has been developed by using the multi-moment finite volume method that ensures the rigorous numerical conservation. To represent the spherical geometry free of polar problems, the cubed-sphere grid is…
We propose and analyze a structure-preserving parametric finite element method (SP-PFEM) to simulate the motion of closed curves governed by area-conserved generalized mean curvature flow in two dimensions (2D). We first present a…
We propose an unconditionally energy-stable, orthonormality-preserving, component-wise splitting iterative scheme for the Kohn-Sham gradient flow based model in the electronic structure calculation. We first study the scheme discretized in…
Common techniques for the spatial discretisation of PDEs on a macroscale grid include finite difference, finite elements and finite volume methods. Such methods typically impose assumed microscale structures on the subgrid fields, so…
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…
We propose and analyze two convection quasi-robust and pressure robust finite element methods for a fully nonlinear time-dependent magnetohydrodynamics problem. Both methods employ the $H_{\rm div}$ conforming BDM element coupled with an…
We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the…
In this work a new finite element based Method of Relaxed Streamline Upwinding is proposed to solve hyperbolic conservation laws. Formulation of the proposed scheme is based on relaxation system which replaces hyperbolic conservation laws…
In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the P\'eclet number. In this situation, computational instabilities occur, both for steady and…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…
We consider a sharp interface formulation for the multi-phase Mullins-Sekerka flow. The flow is characterized by a network of curves evolving such that the total surface energy of the curves is reduced, while the areas of the enclosed…
A conservative finite-volume framework, based on a collocated variable arrangement, for the simulation of flows at all speeds, applicable to incompressible, ideal-gas and real-gas fluids is proposed in conjunction with a fully-coupled…
Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…