Serving the Numerical Simulation community since 1989 
Welcome to the official blog of ESRD, where we discuss trending topics in numerical simulation and in the CAE industry.
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.
In engineering sciences, we classify mathematical models as ‘proper’ or ‘improper’ rather than ‘scientific’ or ‘pseudoscientific’. A model is said to be proper if it is consistent with the relevant mathematical theorems that guarantee the existence and, when applicable, the uniqueness of the exact solution. Otherwise, the model is improper. At present, the large majority of models used in engineering practice are improper. Following are examples of frequently occurring types of error, with brief explanations.
Smart Engineering Simulation Applications, (SESA or Sim Apps), are software tools crafted by expert analysts to standardize recurring simulation tasks. Learn more about how Sim Apps and AI tools can work together to enhance engineering simulation workflows.
Engineering students and professionals alike want to know: are singularities “real”? And if so, when they appear in our solutions, what are we supposed to do with them?
Regarding the practical question of what to do with singularities; we need to distinguish between cases where singularities are just nuisances and where a singularity is the object of simulation.
From all of us at ESRD, we wish you a very happy holiday season! We truly feel that each and every one of our users are part of the ESRD family and we are incredibly grateful to get to work with all of you.
There is much we are thankful for as we approach the end of the year, and we’d like to take a moment to acknowledge some of the reasons we’re looking back fondly on 2023…
A mathematician delivered a keynote presentation at an engineering conference some years ago. At the coffee break, following the presentation, a highly respected senior developer of a legacy finite element code, remarked: “I do not understand why the speaker was so worried about singularities. We never see them.”
The remark highlights the lack of a common language between the pre-scientific notion of finite element modeling and finite element analysis, which is a branch of applied mathematics. Read why mathematicians and engineers alike should “worry” about singularities.
© 2026 · Engineering Software Research & Development, Inc. | Terms & Conditions | Privacy & Cookie Policy | Software License Agreement | Software Maintenance and Technical Support Policy