Combinatorial scientific computing (CSC) is a relatively recently coined term (towards the end of 2002) for interdisciplinary research spanning discrete mathematics and scientific computing. It refers to the development, application, and analysis of combinatorial algorithms to enable scientific computing applications. Here the word "enable" is used intentionaly because for example if one does not order (using graph theoretical notions) sparse matrices properly, then the fill-in and time would be prohibitive in LU decomposition. The standard tools of the trade and the standard problems of the domain, among many other tools and problems, include graph models for LU, load balancing and partitioning for efficient parallelization using hypergraph and graph models, graph coloring methods for automatic differentiation, graph embedding-based methods and theoretical results to design and analyze preconditioners for iterative methods (for the solution of linear systems).
The general approach is to identify performance issues (all sorts: memory use, parallel speed up, the rate of convergence of a method etc.) in a scientific computing problem and to develop combinatorial algorithms and models to alleviate the issue.