Multi-Fidelity Monte-Carlo Estimation of Satellite Drag in Very-Low-Earth Orbit

Abstract

Very-low-Earth orbit drag uncertainty quantification in the rarefied/transitional Knudsen-number regime requires estimating not only the mean drag coefficient but also higher-order moments under atmospheric variability, which becomes prohibitively expensive when high-fidelity kinetic solvers are required. This work develops a multi-fidelity Monte Carlo (MFMC) estimator for the drag coefficient using a DSMC solver (PICLas) as the high-fidelity model and two free-molecular panel-method variants (ADBSat with Sentman and Cercignani-Lampis-Lord (CLL) gas-surface interaction models) as low-fidelity control variates. We treat E[C_D] and E[C_D^2] as the primary estimation targets and form the physically induced variance only afterwards via Var(C_D)=E[C_D^2]-(E[C_D])^2. High-fidelity reference moments are obtained from long DSMC sequences using objective convergence criteria based on sliding-window stability and 95% confidence intervals. The MFMC implementation is first numerically verified on an analytic toy model with closed-form moments, then assessed on a canonical CubeSat geometry (validation) and on SOAR, GOCE, and CHAMP configurations (verification) under MSIS-derived thermospheric variability and angle-of-attack uncertainty. When low-fidelity correlations are high for both C_D and C_D^2, MFMC reduces the relative RMSE of E[C_D] and E[C_D^2] by factors of several at matched high-fidelity-equivalent cost; improvements for Var(C_D) remain more case-dependent due to cancellation sensitivity. Overall, the study identifies practical drivers (moment correlations, cost ratios, and weight stability) that govern when panel models serve as effective control variates for DSMC-based drag uncertainty quantification.