This volume comprises the second part of the proceedings of the 10th International Conference on Finite Volumes for Complex Applications, FVCA, held in Strasbourg, France, during October 30 to November 3, 2023.

The Finite Volume method, and several of its variants, is a spatial discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods are also built to preserve some properties of the continuous equations, including maximum principles, dissipativity, monotone decay of the free energy, asymptotic stability, or stationary solutions. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differentialequations becomes particularly important for multiphysics and multiscale applications. In recent years, the efficient implementation of these methods in numerical software packages, more specifically to be used in supercomputers, has drawn some attention.

The first volume contains all invited papers, as well as the contributed papers focusing on finite volume schemes for elliptic and parabolic problems. They include structure-preserving schemes, convergence proofs, and error estimates for problems governed by elliptic and parabolic partial differential equations.

This volume is focused on finite volume methods for hyperbolic and related problems, such as methods compatible with the low Mach number limit or able to exactly preserve steady solutions, the development and analysis of high order methods, or the discretization of kinetic equations.

Comprehensive overview of the state of the art Both theoretical and applied aspects are covered Authors are leading researchers from the community

Inhalt
W. Aboussi, M. Ziggaf, I. Kissami and M. Boubekeur_A finite volume scheme with a diffusion control parameter on unstructured hybrid mesh: application to two-dimensional Euler equations.- L. Baroukh and E. Audusse, Flow of Newtonian fluids in a pressurized pipe.- W. Barsukow, Truly multi-dimensional all-speed methods for the Euler equations.- T. Bellotti, Monotonicity for genuinely multi-step methods: results and issues from a simple lattice Boltzmann scheme.- C. Birke and C. Klingenberg, A Low Mach Number Two-speed Relaxation Scheme for Ideal MHD Equations.- G. Birke, C. Engwer, S. May and F. Streitbürger, Domain of Dependence stabilization for the acoustic wave equation on 2D cut-cell meshes.- J. Bussac and K. Saleh, Numerical simulation of a barotropic two-phase flow model with miscible phases.- S. Chu and A. Kurganov, Local Characteristic Decomposition Based Central-Upwind Scheme for Compressible Multifluids.- F. Dubois and J. Antonio Rojas-Quintero, Simpson's quadrature for a nonlinear variational symplectic scheme.- E. Chudzik, C. Helzel and Yanick-Florian Kiechle, An Active Flux Method for the Vlasov-Poisson System.- M. Dumbser, S. Busto and A. Thomann, On thermodynamically compatible finite volume schemes for overdetermined hyperbolic systems.- M. Ferrand, Jean-Marc Hérard, T. Norddine and S. Ruget, A scheme using the wave structure of second-moment turbulent models for incompressible flows.- T. Galié, S. Kokh, Ahmad El Halabi, K. Saleh and P. Fernier, Study of a Numerical Scheme with Transport-Acoustic Operator Splitting on a Staggered Mesh.- C. Fiorini, Uncertainty propagation of the shock position for hyperbolic PDEs using a sensitivity equation method.- C. Ghosn, T. Goudon and S. Minjeaud, Staggered MUSCL scheme for Euler equation.- M. Girfoglio, A. Quaini and G. Rozza, GEA: a new finite volume-based open source code for the numerical simulation of atmospheric and ocean flows.- P. Helluy and R. Hélie, Stable second order boundary conditions forkinetic approximations.- A. Iollo, G. Puppo and A. Thomann, Two-dimensional linear implicit relaxed scheme for hyperbolic conservation laws.- H. H. Holm and F. Beiser, Reducing Numerical Artifacts by Sacrificing Well-Balance for Rotating Shallow-Water Flow.- G. Jomée and Jean-Marc Hérard, Relaxation process in an immiscible three-phase flow model.- J. Jung, I. Lannabi and V. Perrier, On the convergence of the Godunov scheme with a centered discretization of the pressure gradient.- J. Keim, A. Schwarz, S. Chiocchetti, A. Beck and C. Rohde, A Reinforcement Learning Based Slope Limiter for Two-Dimensional Finite Volume Schemes.- S.-C. Klein, Essentially Non-Oscillatory Schemes using the Entropy Rate Criterion.- T. Laidin and T. Rey, Hybrid Kinetic/Fluid numerical method for the Vlasov-Poisson-BGK equation in the diffusive scaling.- M. Mehrenberger, L. Navoret and Anh-Tuan Vu, Composition schemes for the guiding-center model.- M. Ndjinga and K. Ait-Ameur, TVD analysis of a (pseudo-)staggered scheme for the isentropic Euler equations.- F. Peru, Backward reconstruction for non resonant triangular systems of conservation laws.- Sri Redjeki Pudjaprasetya and P. V. Swastika, Two-layer exchange flow with time-dependent barotropic forcing.- G. Schnücke, Split Form Discontinuous Galerkin Methods for Conservation Laws.- L. Renelt, C. Engwer and M. Ohlberger, An optimally stable approximation of reactive transport using discrete test and infinite trial spaces.- A. Toufaili, S. Gavrilyuk, O. Hurisse and Jean-Marc Hérard, An hybrid solver to compute a turbulent compressible model.