The goal of this work is to describe the dynamics of DNA knots with excess link in an ionized fluid. To do so, we employ two models: 1. the Generalized Immersed Boundary (GIB) method, which is a deterministic method that accounts for the fluid, structure interaction of an immersed DNA molecule in an ionized fluid; 2. the Stochastic Generalized Boundary (SGIB) Method, which is an extension of the GIB method that also takes into account the random thermal fluctuations within the fluid. Using the GIB and SGIB methods, we numerically explore the energy landscape of a closed DNA segment with excess twist in a trefoil knot configuration. We first analyze the symmetry of stable knotted equilibrium configurations, approximate saddle configurations, and examine the elastic energy throughout the deterministic process. We then use the SGIB method to model DNA knot dynamics as a continuous time Markov chain. We classify boundaries within the energy landscape using the Procrustes distance. Finally, we obtain a steady state distribution for the Markov process given a fixed linking number and compare this to energy estimates obtained from the GIB method.