Serving the Numerical Simulation community since 1989 
At present, a very substantial unrealized potential exists in numerical simulation. Simulation technology has matured to the point where management can realistically expect the reliability of predictions based on numerical simulations to match the reliability of observations in physical experimentation. This will require management to upgrade simulation practices through exercising simulation governance.
Digital transformation is a multifaceted concept with plenty of room for interpretation. Its common theme emphasizes the proactive adoption of digital technologies to reshape business practices with the goal of gaining a competitive edge. The scope, timeline, and resource allocation of digital transformation projects depend on the specific goals and objectives. Here, we address digital transformation in the engineering sciences, focusing on numerical simulation.
The idea of a digital twin originated at NASA in the 1960s as a “living model” of the Apollo program. When Apollo 13 experienced an oxygen tank explosion, NASA utilized multiple simulators and extended a physical model of the spacecraft to include digital simulations, creating a digital twin. This twin was used to analyze the events leading up to the accident and investigate ideas for a solution. The term “digital twin” was coined by NASA engineer John Vickers much later. While the term is commonly associated with modeling physical objects, it is also employed to represent organizational processes. Here, we consider digital twins of physical entities only.
Models, developed under the discipline of VVUQ, can be relied on to make correct predictions within their domains of calibration. However, model development projects lacking the discipline of VVUQ tend to produce wrong models.
Certification by Analysis (CbA) uses validated computer simulations to demonstrate compliance with regulations, replacing some traditional physical tests. CbA allows for exploring a wide range of design scenarios, accelerates innovation, lowers expenses, and upholds rigorous safety standards. The key to CbA is reliability. This means that the data generated by numerical simulation should be as trustworthy as if they were generated by carefully conducted physical experiments. To achieve that goal, it is necessary to control two fundamentally different types of error; the model form error and the numerical approximation error, and use the models within their domains of calibration.
In the engineering sciences, mathematical models are based on the equations of continuum mechanics, heat flow, Maxwell, Navier-Stokes, or some combination of these. These equations have been validated and their domains of calibration are generally much larger than the expected domain of calibration of the model being developed. In the terminology introduced by Lakatos, the assumptions incorporated in these equations are called hardcore assumptions, and the assumptions incorporated in the other constituents of a model are called auxiliary hypotheses. Model development is concerned with the formulation, calibration, and validation of auxiliary hypotheses.
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