Shock Dynamics Flows Dataset Creation using Explicit and Implicit Finite Difference Solvers

In this study, we generated a shock dynamics dataset to solve the one-dimensional time-dependent viscous Burgers equation using explicit and implicit finite difference methods. We systematically varied the initial and surface conditions, including fixed (Dirichlet), flow (Neumann), and periodic (Periodic) conditions. These variations enabled us to simulate a range of flow regimes, from shock evolution to diffusion and dissipation. By comparing the numerical behavior of explicit and implicit methods, we were able to quantify their stability, accuracy, and computational performance. The resulting dataset provides a controlled environment for evaluating numerical solvers and serves as a foundation for future data-driven modeling of nonlinear transport phenomena.