The effect of roughness should be taken into consideration in the lubrication and geometric design of heavy-duty machine elements. Deterministic simulation techniques have been developed for the investigation of point-contact mixed-lubrication problems. Such approaches should also been extended to deterministic mixed lubrication solutions for journal-bearing conformal-contact systems. However, journal-bearing mixed lubrication involves a much larger area of surface interaction as compared to point contact problems. It is difficult to use similar micro/nano scale meshes directly to journal bearings under the current computer capability. It is a great challenge to develop a new deterministic numerical technique for the mixed lubrication of journal bearing systems with the consideration of the effect of surface roughness design. This paper presents a special technique for deterministic analyses of journal-bearings in mixed lubrication conditions, in which the coarse mesh is used to determine the elastic deformation of the journal bearing, whilst locally refined meshes are used for the effect of roughness. Journal-bearing systems in heavy machinery are often subject to dynamic loading. Therefore, a transient refinement scheme is also introduced.