Many different factors contribute to elapsed runtime of reservoir simulators. Once the cases become larger and more complex, the required wait time for results can become prohibitive. This chapter discusses three features recently introduced into the MRST AD-OO framework to make simulation of large cases more efficient. By analysing the sparsity pattern of the Jacobians for some of the most common operations involved in computing residual flow equations, we have developed different implementations of automatic differentiation that offer better memory usage and requires fewer floating point operations. Using these so-called AD backends ensures (much) faster assembly of linearized systems. Likewise, these systems can be solved much faster by utilizing external packages for linear algebra; herein, primarily represented by the AMGCL header-only C++ library for solving large sparse linear systems with algebraic multigrid (AMG) methods. Last, but not least, the new ``packed problem'' format simplifies the management of multiple simulation cases and enables automatic restart of simulations and an ability for early inspection of results from large batch simulations. Altogether, these features are essential if you are working with bigger simulation models and want timely results that persist across MATLAB sessions.

A reservoir simulator consists of a large set of models and parameters to describe the geology, fluid behavior, wells and surface facilities, and rules and conditions that describe and control the production process. On the numerical side, you have a combination of discretization methods, nonlinear solvers, linearizations, linear solvers, preconditioners, stability and convergence checks, and algorithms for automated time-step selection. The AD-OO framework in MRST is developed to encapsulate all these details, such that on one side it offers industry-grade simulator capabilities, and on the other side a flexible framework for rapid development of new proof-of-concept implementations. This chapter outlines the design philosophy behind AD-OO and explains many of its ingredients in detail. By reading this chapter, you will get an in-depth introduction to all the details you need to make a full-fledge reservoir simulator. The chapter ends with a discussion of three cases: a simple pressure depletion, multisegment representation of instrumented wells, and the full SPE 9 benchmark.