2023/12/20 by Andrea Cavagna, Javier Cristín, Cavagna, Andrea +5 · 2 citations
Engineering · Environmental Science · Physics and Astronomy · #FOS: Physical sciences #Soil Geostatistics and Mapping #Soil and Unsaturated Flow #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2312.13065
openalex publication_date 2023/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Numerical analysis of conserved field dynamics has been generally performed with pseudo spectral methods. Finite differences integration, the common procedure for non-conserved field dynamics, indeed struggles to implement a conservative noise in the discrete spatial domain. In this work, we present a novel method to generate a conservative noise in the finite differences framework, which works for any discrete topology and boundary conditions. We apply it to numerically solve the conserved Kardar-Parisi-Zhang (cKPZ) equation, widely used to describe surface roughening when the number of particles is conserved. Our numerical simulations recover the correct scaling exponents α, β, and z in d=1 and in d=2. To illustrate the potentiality of the method, we further consider the cKPZ equation on different kinds of non-standard lattices and on the random Euclidean graph. This is the first numerical study of conserved field dynamics on an irregular topology, paving the way to a broad spectrum of possible applications.