We describe a new high resolution research model that has been developed for the study and short term prediction of mesoscale weather systems. The model initially is applied to idealized simulations of tropical cyclones. Tropical cyclones possess a range of scales, from meso-alpha down to meso-gamma, and are a robust test of the model at high resolutions. The two major components of a numerical weather prediction (NWP) model are the dynamics and physics kernels. Here, we have concentrated on implementing and testing numerical schemes that have appeared in the recent literature. The focus of this study is on the accuracy and efficiency of using high-order difference schemes. We also assess the performance of two non-oscillatory schemes for scalar advection of positive definite quantities. The results from a range of test cases are presented, culminating in a high resolution simulation of an idealized tropical cyclone. Tests were performed with advection schemes up to 10th order to confirm the need for higher order schemes but also to demonstrate the diminishing returns using schemes beyond 6th order. The scheme with the best overall performance was the 5th order upwind advection scheme with similar order non-oscillatory schemes for fields that have positive definite constraints. In conclusion, we recommend that high-order numerical schemes are implemented as the basis of the dynamics kernel of high resolution NWP models, especially when applied to complex multi-scale flows such as tropical cyclones.