arXiv subjects

Josipa-Pina Milišić

Publications and source records attributed to Josipa-Pina Milišić.

6 recordsLinked to original sources

arXiv2026

An Analytical Review of Model Order Reduction Methodologies of Converter-Dominated Power Systems for Stability Studies

The rapid integration of renewable energy sources is transforming modern electric power systems into converter-dominated networks characterized by complex multi-timescale dynamics and new stability interactions over a wide frequency range. Accurate analysis of these phenomena requires high-fidelity models of transmission networks and power electronic converters, which often result in large-scale differential-algebraic systems with significant computational burden. This paper provides an analytical review of model order reduction techniques for converter-rich power systems, with particular emphasis on the key equations employed in the reduction process. Advantages and limitations of commonly used strategies, including timescale-based singular perturbation, projection-based, operator-based, data-driven, and machine-learning based methods, are discussed. The synthesis highlights key challenges related to harmonic interactions and multi-frequency dynamics, and outlines directions for the development of computationally efficient yet dynamically accurate reduced-order models for future power systems.

eess.SY↗

arXiv2026

Energy dissipation and stability of a finite-volume scheme for two-phase flow models with dynamic capillary pressure

An implicit Euler finite-volume scheme for degenerate pseudo-parabolic cross-diffusion equations is proposed and analyzed. The system describes the dynamics of an unsaturated two-phase flow mixture with dynamic capillary pressure in a porous medium. The numerical scheme is based on a two-point flux approximation that preserves the energy structure, ensures the conservation of total mass, and guarantees strict positivity and boundedness of the water saturation. These properties rely on carefully selected mean functions for the nonlinear components. The existence and uniqueness of a discrete solution and additional mesh-uniform bounds are proved. Numerical experiments in two space dimensions illustrate the effects of the dynamic capillary pressure.

math.NA↗

arXiv2019

Global existence for a two-phase flow model with cross diffusion

In this work we study a degenerate pseudo-parabolic system with cross diffusion describing the evolution of the densities of an unsaturated two-phase flow mixture with dynamic capillary pressure in porous medium with saturation-dependent relaxation parameter and hypocoercive diffusion operator modeling cross diffusion. The equations are derived in a thermodynamically correct way from mass conservation laws. Global-in-time existence of weak solutions to the system in a bounded domain with equilibrium boundary conditions is shown. The main tools of the analysis are an entropy inequality and a crucial apriori bound which allows for controlling the degeneracy.

math.AP↗

arXiv2018

Analysis of a degenerate and singular volume-filling cross-diffusion system modeling biofilm growth

We analyze the mathematical properties of a multi-species biofilm cross-diffusion model together with very general reaction terms and mixed Dirichlet-Neumann boundary conditions on a bounded domain. This model belongs to the class of volume-filling type cross-diffusion systems which exhibit a porous medium-type degeneracy when the total biomass vanishes as well as a superdiffusion-type singularity when the biomass reaches its maximum cell capacity, which make the analysis extremely challenging. The equations also admit a very interesting non-standard entropy structure. We prove the existence of global-in-time weak solutions, study the asymptotic behavior and the uniqueness of the solutions, and complement the analysis by numerical simulations that illustrate the theoretically obtained results.

math.AP↗

arXiv2018

The unsaturated flow in porous media with dynamic capillary pressure

In this paper we consider a degenerate pseudoparabolic equation for the wetting saturation of an unsaturated two-phase flow in porous media with dynamic capillary pressure-saturation relationship where the relaxation parameter depends on the saturation. Following the approach given in [12] the existence of a weak solution is proved using Galerkin approximation and regularization techniques. A priori estimates needed for passing to the limit when the regularization parameter goes to zero are obtained by using appropriate test-functions, motivated by the fact that considered PDE allows a natural generalization of the classical Kullback entropy. Finally, a special care was given in obtaining an estimate of the mixed derivative term by combining the information from the capillary pressure with obtained a priori estimates on the saturation.

math.AP↗

arXiv2013

Entropy dissipative one-leg multistep time approximations of nonlinear diffusive equations

New one-leg multistep time discretizations of nonlinear evolution equations are investigated. The main features of the scheme are the preservation of the nonnegativity and the entropy-dissipation structure of the diffusive equations. The key ideas are to combine Dahlquist's G-stability theory with entropy-dissipation methods and to introduce a nonlinear transformation of variables which provides a quadratic structure in the equations. It is shown that G-stability of the one-leg scheme is sufficient to derive discrete entropy dissipation estimates. The general result is applied to a cross-diffusion system from population dynamics and a nonlinear fourth-order quantum diffusion model, for which the existence of semi-discrete weak solutions is proved. Under some assumptions on the operator of the evolution equation, the second-order convergence of solutions is shown. Moreover, some numerical experiments for the population model are presented, which underline the theoretical results.

math.NA↗