Modeling, Simulation & Analysis

SC Solutions provides modeling and simulation services for a wide range of applications.

We develop physics-based models to accurately capture input-output and internal behavior of various dynamic systems, including industrial equipment and processes.

The models encompass cross-disciplinary areas such as fluid flow, heat and species transport, solid mechanics, rigid and flexible-body dynamics, and electromagnetics.

High-fidelity models, calibrated and validated with experimental data, are used in “what-if” analyses for design modifications, performance analysis, process optimization, and for verifying low-order models.

Low-order models that run faster than real time are developed using various state-of-the-art model-order reduction techniques. These low-order models are implemented in C code and are compiled to execute on various real-time operating systems. These fast low-order models are used in model-based control (MBC) design, for virtual sensing, and as components of digital twins.

Below are some more details about the models and their use.

What are these models?
Our models typically consist of systems of non-linear Ordinary Differential Equations (ODE’s) that describe the underlying physics of the dynamic (time-varying) system to a good approximation. These models range from a few dozen ODE’s to large systems with thousands of ODE’s. Invariably there will be uncertain aspects of the problem, ranging from uncertainty in material properties to uncertainties in the modeled physics of the problem. We typically incorporate physically meaningful adjustable parameters in the model. Adjusting these parameters by comparing simulation results to experimental data (model calibration) helps account for many of these uncertainties.

What types of physics are encapsulated in these models?
Typically, our models encompass heat, flow and species transport, chemical kinetics, and solid mechanics. These are key phenomena in many manufacturing processes, including those for semiconductors and other advanced materials. We also develop models in cross-disciplinary areas such as electromagnetics and optics. Some specific applications include modeling of hot-wall and cold-wall furnaces, thermal stress and deformation, Chemical Vapor Deposition (CVD), Chemical Mechanical Planarization (CMP), Physical Vapor Deposition (PVD), and RF inductive heating.

What tools are used to develop such models?
Some of our models are implemented using commercial tools, while others are developed using SC Solutions’ proprietary in-house modeling software. Our primary tools for developing high-fidelity (high-order) models are:

  • COMSOL Multiphysics, a leading finite element modeling software tool for which SC is a Certified Consultant.
  • MATLAB-based in-house software (control volume) for thermal models. SC is a MATLAB Partner.
  • Other tools used at SC are Thermal Desktop (an interface to SINDA / FLUINT), ANSYS / Fluent, and ADINA.

SC’s fast (low-order) models are implemented in C using SC’s proven proprietary SC-x™ software framework – the latter having been developed for implementing real-time MBC’s.

SC also uses a novel ray-tracing software package that was developed in-house and validated over two decades of use. It incorporates directional radiative properties, multi-band radiation, and semi-transparent media. It has been specifically designed to accurately model radiation emitted from relatively small surfaces.

How would modeling be useful to me?
There are many ways that the models we develop are useful to our customers:

  • Control design: Our feedback and feedforward controllers are designed using dynamic physics-based models. High-order models undergo model reduction in order to produce a “control relevant” model that runs simulations in real time while retaining sufficient accuracy for the desired set of state variables. This approach enables a very efficient control design process and results in high-performance dynamic controllers.
  • Equipment design and performance optimization: SC works with equipment manufacturers from the early stages of design of the next-generation prototype. The designs are tested in closed-loop simulation for performance, and necessary design changes are incorporated. The iterative process is continued until an optimal design that meets the performance specifications is obtained before commencing on the expensive process of building the equipment prototype. Additionally, models are used to determine the optimal number of sensors and their locations, and to determine the optimal number of actuator groupings.
  • Virtual sensing: The models can be used as virtual sensors where measurements made at some easily accessible locations are used to accurately estimate the state at difficult-to-measure points by exploiting the dynamic interrelationship between the states in the equipment model. An added advantage of this approach is that the number of sensors can be reduced, which decreases costs while increasing system robustness.
  • Equipment fault diagnostics and health monitoring: Specific equipment (e.g., a specific model of a furnace) may be characterized by a set of model parameters whose values will be restricted to a determinable range for a system operating normally. Parameter excursion out of that range is a sign of equipment mismatch and possibly an existing or impending problem. The specific parameter (or parameters) thus becomes an indicator of the subsystem where the problem may have occurred (e.g., heater degradation, cooling water supply variation, etc.). Such an approach can improve root-cause analysis for equipment.
  • Digital Twin: A digital twin is a complete dynamic model of existing equipment whose model parameters are continually updated with sensor data. A digital twin simulation must run in real-time or faster and describe the system’s change in temporal behavior with acceptable accuracy. The fast, low-order models that we develop would make up key components of the system’s digital twin. The digital twin may be used for a wide range of applications including process optimization, fault diagnostics, tool-to-tool matching, performance assurance, and predictive maintenance.

How much would it cost to model my problem?

  • The cost depends on the complexity of the problem, both geometrical and the multiphysics involved, as well as the scope of the effort. Our modeling projects range from those that involve a few days to ones that require several person-weeks of effort. Additionally, we have been involved in longer duration R&D programs spanning a year or two that have involved equipment design or modification, as well as process improvement.
  • We address the problem in a systematic manner and ensure that we are on the same page as our customer regarding the details and assumptions involved in developing the model. A modeling effort is generally broken down into multiple sequential tasks, and hours assigned to each task in the proposal.
  • We work closely with our customers and update them with the results of each task as they become available. This approach provides flexibility to our customers, and enables them to modify the scope and direction of the effort at any stage.

How are modeling results delivered to customers?
For engineering consulting work, we generally provide results of model simulations as presentations. Depending on the scope of the work, we may write a report. When a model is developed with commercial tools, we can provide the model at the request of the customer and provide instructions to run simulations with it.