M4Dynamics™ is a Toronto based consulting and software development company specialized in Multiphysics and Solution Thermodynamics Simulations Analysis, Development of custom built applications or physics models and COMSOL® Training.



M4Dlib is an add on tool developed by M4Dynamics™ to enable COMSOL® to solve coupled Multiphysics and Thermodynamic problems involving complex multicomponent multiphase reactive systems. With M4Dlib, the simulation of ideal and non-ideal solution systems is coupled to COMSOL Multiphysics® by adding Gibbs Free Energy minimization routines to COMSOL®.



M4Dynamics™ specializes in Thermodynamic Simulation, Chemical Engineering, Heat Transfer, Fluid Flow, Equation Based Modeling and Custom end-user ready Application development.

M4Dynamics™ serves Industries in the areas of Chemical Processing, Extractive Metallurgy, Mining with over 15 years of experience working in numerical simulation of real world problems in research and development and industrial applications.


Multiphysics & Thermodynamics Simulation



Our Next Free Workshop  in Toronto


Thermodynamics-Based Process Simulation Workshop


Oct 20th, 2017

for more Information click here

for Registration, click here


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Multiphysics and Thermodynamic Simulation

At M4Dynamics™ we have specialized in solving multiphysics problems involving single or coupled heat transfer, mass transfer, fluid flow or chemical reactions. We will analyze your problem by understanding the processes involved and applying the required fundamental physics in order to generate the maximum value solution.

In some cases, involving multicomponent multiphase non-ideal systems, it is necessary to incorporate solution thermodynamic calculations to solve the problem either through direct thermodynamic process simulation or by coupling thermodynamics to multiphysics simulation. For that reason, we have developed M4Dlib™ an external function library for COMSOL® that allows solving complex and thermodynamic intensive problems within COMSOL Multiphysics® without the need of interfacing with external third party software.

Our commitment is to deliver high quality and highly specialized simulation solutions with fast turnaround by working closely with the client and bringing our extensive experience in process simulation.

Customs Simulations Applications

COMSOL® Applications

We take full advantage of the new COMSOL® Application Builder and COMSOL Server™ capabilities and develop end-user ready applications that can be deployed to the client to be run locally or over the network, making it available across the entire organization and accessible from anywhere in the world. This new approach builds on our previous experience in building COMSOL® applications based on MATLAB based GUI and software development.

Thermodynamic Process Simulators

When only thermodynamic process simulation is necessary and sufficient to solve the problem at hand, we can develop a custom built application using the local equilibrium concept to simulate complex industrial processes. This type of simulation is delivered in the form of a stand alone application that can be run by the end-user from a local computer.

Customs Physics Models

In some instances, it is necessary to simulate problems that are not described by any of the available physics modules. Our Experience in having developed PDE based models for such types of simulations will allow M4Dynamics™ to provide a solution when a new physics model is needed either by creating a PDE based model or a new physics interface using COMSOL®’s Physics Builder.

Note that depending on the solution provided, the client might be required to own a valid COMSOL Multiphysics® License. To discuss further requirements, please contact us.

Thermodynamic Database Development

A successful simulation of a complex thermochemical system involving coupled Solution Thermodynamics and Multiphysics depends on the description of the Thermodynamic System including all relevant compounds and solution models. Basic database of pure or stoichiometric compounds is provided by M4Dynamics™ in the form of an input thermodynamic database file.

When known or published solution parameters are available to the client, M4Dynamics™ will generate the required thermodynamic database files or will perform the required literature search and database generation based on published data.



M4Dynamics™ own’s Product designed to simulate Coupled Multiphysics and Solution Thermodynamics problems from within the COMSOL Multiphysics® Desktop Environment by simply calling an external function.

M4Dlib™ is a dynamic library for Windows and OS-X that is used from COMSOL® as an “external function”.

M4Dlib™ handles the input thermodynamic database files as well as all the complex Equilibrium Thermodynamics routines for multiphase ideal or non-ideal systems and provides the results to COMSOL® without the need of interfacing with third party thermodynamic softwares.

The integration of M4Dlib to COMSOL Multiphysics® by a simple call to an external function makes the process of simulating complex chemical systems involving phase change or non ideal solution thermodynamics extremely simple, allowing the user to speed up the development and simulation process.


Expand COMSOL Multiphysics® Simulation Power to Include Solutions Equilibrium Thermodynamic to your Models with M4Dlib™!







Our Next COMSOL® Training in Ottawa


2-days Intensive Training,  Nov 8th-9th, 2017

for more information and registration, click here

At M4Dynamics™ we believe in the importance of the client’s involvement in the analysis of multiphysics problems either by providing full autonomy to fully use COMSOL Multiphysics® and M4Dynamics™ Products in house or by actively participating in the consulting process with full understanding and criticism of the capabilities and limitations of the numerical tools used. That way, the evaluation of results and the final outcome of any consulting service is enhanced for both parties.

Contact Us

Company name:        M4 Dynamics Inc.

1 (647) 518 0430

1 Yonge Street, Suite 1801, Toronto, ON,

 M5E 1W7, Canada

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