Denis V. Esipov (personal page)

Vice director for research, PhD

Federal Research Center for Information and Computational Technologies (FRC ICT)
Academician M.A. Lavrentiev avenue, 6,
630090, Novosibirsk, Russia

Phone: +7 383 334 9130
Fax: +7 383 330 6342
Email :

Senior researcher (2014 - today) at the Laboratory of mathematical modeling of ICT SB RAS (Head of the laboratory is prof. Sergey Cherny)
Senior teacher (2018 - today) at the Chair of Mathematical Modelling of the Novosibirsk State University (see Teaching)

Research interests

  • Computational mechanics
  • Simulation of disperse (dense) flows with relatively big particles
  • Simulation of the chemically reacting flows.
  • Mathematical modelling of fluid flow, elasticity, and fracturing problems.
  • Simulation of the hydraulic fracturing process.
  • Numerical methods (Finite difference (volume) method, FEM, BEM, DEM, etc)

Recent activities

I with my colleagues are performing three research projects:

  • Numerical simulation of disperse fluid flows in channels with relatively big particles
    We are interested in rheology changes, and jamming conditions depended on particle shapes, its density, and configuration of the channel. Now we have developed 3D numerical model based on Navier-Stockes equations and the system of motion and rotation equations for particles. To solve Navier-Stockes equations we use the immersed boundary method with the SIMPLE like algorithm on the Cartesian staggered grid. To solve a system of motion equations we use Euler’s integration method with smaller time steps to account particle collisions and friction between them. An example of typical computed fluid flow pattern you can see above on the page. This study was supported by the Russian Science Foundation (grant No. 17-71-20139). Another problem of interest within the frame of this project is the direct numerical simulation of the Boycott effect. We are doing this part of the study in collaboration with prof. Vladimir Shelukhin.
  • Development of the model of the chemical cracking reactor for heavy oil and its residuals
    We have proposed realistic, but not so expensive numerical model of mixture flow in the cracking reactor. We plan to incorporate several models of chemical reactions and validate them. The results could be applied to the optimization of the cracking process and the design of cracking reactors. This investigation is supported by the Russian Foundation for Basic Research (grant No. 20-01-00440).
  • Development of models of hydraulic fracturing taking into account realistic mechanics near the fracture tip
    We plan to improve our fully coupled numerical models of hydraulic fracturing by the recent developments of asymptotic solutions. Using these hybrid numerical models we plan to investigate the mechanics of aroused processes and evaluate their influence on the velocity and trajectory of the fracture.

Past activities

Chairman (2012 - 2020) of the Seminar "Information and Computing Technologies for Problems of Decision Support"

I have took part in the work of the BIRS Workshop on Hydraulic Fracturing: Modeling, Simulation and Experiment held in Banff (Canada), June 3-8, 2018, and organized by Emmanuel Detournay, Anthony Peirce, Andrew Bunger, Egor Dontsov, and Dmitry Garagash. My talk was "The fully coupled 3D numerical model of hydraulic fracturing: ways to improve and possible applications". Here is the video of it.

I have took part in the organization of the "Numerical Simulation of Hydraulic Fracturing" minisymposium on the 14th U.S. National Congress on Computational Mechanics held in Montreal (Canada), July 17-20, 2017. I am glad to make it with Anthony Peirce, Sergey Cherny, and Egor Dontsov as well as Robert Gracie, Armando Duarte, and Erfan Sarvaramini.

For students

Today I have the interest to make a valuable research in the fields presented above. Feel free to communicate me if you are interested in cooperation. Also, see my old internship proposal (2017) for foreign students in the Novosibirsk State University.


Cherny S.G., Lapin V.N., Esipov D.V., Kuranakov D.S. Methods of modeling of initiation and propagation of fractures. — Novosibirsk: SB RAS, 2017. — 312 p. — in Russian.

In this book, we consider the 3D numerical models of fracture initiation from cavities as well as fracture propagation caused by viscous fluid pumping (hydraulic fracturing). The book starts by describing of mathematical models of hydraulic fracturing. Then, there are sections devoted to the original model of the numerical construction of incipient fracture if some breakdown conditions are satisfied. After that, we describe the fully coupled 3D model of hydraulic fracturing, which takes into account non-Newtonian fluid flow in the fracture, elastic deformation of the rock caused by fluid pressure, and the fracturing of the rock. There are verification, and validation of developed mathematical methods, and numerical algorithms. Also, the book has a lot of figures presenting results of a large number of numerical computations.

Main publications


I give a course at the Mechanics and Mathematics Faculty of the NSU: seminar classes on "Numerical methods". The classes go in the 5th and 6th semesters. In 5th semester, the course is devoted to fundamentals of numerical methods for solving ODE problems. Usually we consider initial value problems (IVP) for the first order and second order ODEs, and boundary value problem (BVP) for linear second order ODEs. In terms of numerical methods, we concentrate on the Runge-Kutta, Adams-Bashforth, shooting and finite difference methods. In 6th semester, we deal with numerical methods for PDE problems like initial boundary value problems (IBVP) for 1D and 2D heat equations as well as IBVP for advection (transport) and inviscid Burgers' equations.

In 2020, I have started to give the annual special course "Boundary element methods". Classes go on Fridays at 16:20 in the room 4222. To make a first impression on the boundary element methods, I recommend looking into Wikipedia.

Here is a draft of the book "Computational methods in problems and exercises" (in Russian). The book contains problems usually considered in seminar classes.

Here are two useful programs to draw 2D and 3D plots for practical classes, which I gave in the past.

  • Plot2d is a simple program written in c++ to draw 2D plots.
  • Plot3d is a simple program written in c++ to draw 3D plots.

Both programs need SDL2.0 library.