Core Concepts
Applying the multilevel Monte Carlo method reduces computational costs in uncertainty quantification for the Henry problem.
Abstract
The content discusses the application of the multilevel Monte Carlo (MLMC) method to address uncertainty in density-driven flow problems, focusing on salinisation of coastal aquifers. It explores modeling uncertain parameters like porosity, permeability, and recharge using random fields. The MLMC method is shown to reduce computational and storage costs by solving scenarios on multi-level spatial and temporal meshes. Various numerical experiments are conducted to analyze mean values, variances, and uncertainties in mass fractions at different points and subdomains.
Abstract:
Investigating MLMC method for density-driven flow problems.
Modeling uncertain parameters with random fields.
Reducing computational costs through multi-level spatial and temporal meshes.
Introduction:
Applicability of MLMC to density-driven flow problems.
Challenges with input uncertainties propagation.
Modeling:
Use of random fields for uncertain porosity, permeability, and recharge.
Implementation details for modeling hydrogeological properties.
Numerical Methods:
Discretization techniques for deterministic problem solution.
Utilizing implicit Euler method with time discretization.
Multilevel Monte Carlo:
Telescoping sum approach for estimating expected values efficiently.
Optimization of sample sizes across different levels.
Numerical Experiments:
Test A1:
Mean value and variance visualization of mass fraction.
Test A2:
Analysis of mean and variance changes at specific points.
Stats
Unknown porosity = 0.35 [-]
Permeability = 18.8571 x 10^-6 [m^2 · s^-1]
Density of pure water = 1000 [kg · m^-3]
Density of brine = 1024.99 [kg · m^-3]
Viscosity = 10^-3 [kg · m^-1 · s^-1]
Quotes
"The standard methods such as the Monte Carlo or surrogate-based methods is a good choice."
"We demonstrate that by solving the Henry problem on multi-level spatial and temporal meshes, the MLMC method reduces the overall computational and storage costs."