Some Observations on Thermodynamic Basis of Pressure Continuum Condition and Consequences of Its Violation in Discretised CFD

  • A. W. DateEmail author


CFD is concerned with solution of Navier–Stokes (NS) equations in discretised space. It is important, therefore, to ensure that the discretised equations and their solutions obey the continuum condition embedded in Stokes’s stress–strain laws for an isotropic continuum fluid. In this paper, it is shown that adherence to this condition leads to three important conceptual/algorithmic outcomes: 1. Prevention of zig-zag pressure distribution when NS equations are solved for incompressible flow of a single fluid on colocated grids. 2. Prevention of loss of volume/mass at large times when NS equations are solved for interfacial incompressible flows of multi-fluids within single-fluid formalism. 3. Evaluation of surface tension force in interfacial flows without using phenomenology embedded in the definition of the surface tension coefficient. All the above benefits are justified on the basis of a thermodynamic principle rarely invoked in discretised CFD. A few problems are solved by way of case studies.


Stokes’s stress rate of strain laws Single-phase fluids Interfacial flows Smoothing pressure correction 



It is a privilege for me to contribute to this volume in honour of Prof. D. B. Spalding to whom, in 2004, I sent the initial draft of my book [6] to seek his approval of the contents of the book. He not only read the draft but also gave me a task to solve a 1D problem of highly resisted flow through a porous medium. He solved the problem himself by using what he called Date-Colocated procedure using the PHOENICS code. Over exchange of four emails, he was satisfied that my solutions and his were in agreement. I have included with pride that 1D problem in my book. Material of section 3 was developed during sponsorship of Project No: 2005/36/47/BRNS by the Board of Research in Nuclear Science, Department of Atomic Energy, Govt of India. Contribution of Dr. Kausik Nandi, Scientist F, BARC is gratefully acknowledged.


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentIIT BombayMumbaiIndia

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