Flooding is the most impactful natural hazard of all weather-related events in terms of fatalities and material costs. Due to global warming, future flooding frequency, magnitude, and associated impacts are projected to increase. Numerical models that solve 2-dimensional (2D) shallow water equations (SWE) represent the most comprehensive approach to simulate all types of flooding, such as pluvial, fluvial, and coastal flooding, and their compounding effects. It is computationally expensive to solve 2D SWE at a sub-kilometer resolution at regional and global scales, thus simplifications of SWE (e.g., kinematic and diffusion wave equations, or their 1D derivation) are used to improve computational efficiency. Although models with simplified physics can simulate streamflow accurately, they typically do not capture the inundation extent well. In this study, we used a variable resolution 2D SWE model to reproduce 2017 Houston flooding event during Harvey hurricane. Variable resolution meshes with different levels of topographic details were created using JIGSAW from a base 30m light detection and ranging (LiDAR) dataset. Simulation accuracy and computational efficiency were evaluated for different meshes with respect to the finest resolution of 30 m. Specifically, simulations with variable resolution mesh, with a size less than 2% of the 30m regular mesh, were able to capture over 90% of the spatial variation of simulated inundation depth using the 30m regular mesh. Our results facilitate large scale applications of 2D SWE, for example, replacing the simplified river routing model within Earth System Models.