2023/04/02 by Maria Lukacova -- Medvidova, Medvidova, Maria Lukacova --, Bangwei She +3
Economics, Econometrics and Finance · Mathematics · #65C05 #65M12 #76N06 #80M31 #80M60 #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2304.00594
openalex publication_date 2023/04/02 · openalex created_date 2023/04/06 · openalex updated_date 2026/08/01
In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fourier system. The Monte Carlo method, which is frequently used for the approximation of statistical moments, is combined with a suitable deterministic discretisation method in physical space and time. Under the assumption that numerical densities and temperatures are bounded in probability, we prove the convergence of random finite volume solutions to a statistical strong solution by applying genuine stochastic compactness arguments. Further, we show the convergence and error estimates for the Monte Carlo estimators of the expectation and deviation. We present several numerical results to illustrate the theoretical results.