Realistic sound simulation plays a critical role in many applications. A key element in sound simulation is the room impulse response (RIR), which characterizes how sound propagates from a source to a listener within a given space. Recent studies have applied neural implicit methods to learn RIR using context information collected from the environment, such as scene images. However, these approaches do not effectively leverage explicit geometric information from the environment. To further exploit the potential of neural implicit models with direct geometric features, we present Mesh-infused Neural Acoustic Field (MiNAF), which queries a rough room mesh at given locations and extracts distance distributions as an explicit representation of local context. Our approach demonstrates that incorporating explicit local geometric features can better guide the neural network in generating more accurate RIR predictions. Through comparisons with conventional and state-of-the-art baseline methods, we show that MiNAF performs competitively across various evaluation metrics. Furthermore, we verify the robustness of MiNAF in datasets with limited training samples, demonstrating an advance in high-fidelity sound simulation.