2021/02/11 by Raimund Bürger, Arbaz Khan, Bürger, Raimund +5
Engineering · #65M60 #76R50 #76S05 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2102.05819
openalex publication_date 2021/02/11 · openalex created_date 2021/02/15 · openalex updated_date 2026/07/28
The analysis of the double-diffusion model and H(div)-conforming method introduced in [Bürger, Méndez, Ruiz-Baier, SINUM (2019), 57:1318--1343] is extended to the time-dependent case. In addition, the efficiency and reliability analysis of residual-based \it a posteriori error estimators for the steady, semi-discrete, and fully discrete problems is established. The resulting methods are applied to simulate the sedimentation of small particles in salinity-driven flows. The method consists of Brezzi-Douglas-Marini approximations for velocity and compatible piecewise discontinuous pressures, whereas Lagrangian elements are used for concentration and salinity distribution. Numerical tests confirm the properties of the proposed family of schemes and of the adaptive strategy guided by the \it a posteriori error indicators.