Continuous Data Assimilation for Displacement in a Porous Medium

TL;DR

This paper introduces a continuous data assimilation algorithm for modeling miscible flow in porous media, demonstrating exponential convergence of the approximate solution to the true solution using sparse measurements.

Contribution

It presents a novel continuous data assimilation method that effectively reconstructs flow solutions in porous media without initial conditions, validated through numerical examples.

Findings

Approximate solutions converge exponentially to true solutions.

Sparse measurements suffice for accurate data assimilation.

Numerical examples confirm the algorithm's effectiveness.

Abstract

In this paper we propose the use of a continuous data assimilation algorithm for miscible flow models in a porous medium. In the absence of initial conditions for the model, observed sparse measurements are used to generate an approximation to the true solution. Under certain assumption of the sparse measurements and their incorporation into the algorithm it can be shown that the resulting approximate solution converges to the true solution at an exponential rate as time progresses. Various numerical examples are considered in order to validate the suitability of the algorithm.