<p>Due to the considerable challenge of automatically generating high-quality feature-aligned hexahedral meshes, engineers in industrial simulation have recently turned to a relaxation of the problem, namely hex-dominant meshing, which improves robustness by introducing a small number of non-hexahedral elements. However, most existing algorithms focus on element quality and hexahedral proportion, paying little attention to the hexahedral element distribution quality, a key practical requirement in industrial simulations. To address this issue, this paper proposes an approach to hex-dominant meshing with high-quality hexahedral element distribution, as well as a novel distribution quality metric for evaluating hex-dominant meshes. The algorithm first uses a volumetric frame field to robustly and maximally identify sweepable regions within the input geometry. Each such region is then converted into a strictly sweepable volume by reconstructing its boundary interfaces between regions via oriented bounding box optimization. Finally, high-quality meshes are generated inside sweepable volumes using the sweeping method, whereas hex-dominant meshes are produced in unsweepable volumes via a tetrahedral aggregation strategy. Experimental results demonstrate that the proposed method generates hex-dominant meshes with superior distribution quality, outperforming existing approaches.</p>