welcome to my website

Denis Viktorovich Esipov

PhD, Senior researcher in the Kutateladze Institute of Thermophysics, SB RAS.
Senior teacher (2018 Jul - today) at the Chair of Mathematical Modelling of the Novosibirsk State University (see "For students" section)


Ac. Lavrentieva ave., 1,
Novosibirsk, Russia, 630090

My 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)

My colleague and I 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.

Flow with spherical particles in the flat channel

Fully 3D hydraulic fracture propagation

Stresses in the Francis turbine

Octotree for multipole expansion in FMM BEM

Main publications

Lapin V.N., Esipov D.V. Simulation of proppant transport and fracture plugging in the framework of a radial hydraulic fracturing model // Russian Journal of Numerical Analysis and Mathematical Modelling. — 2020. — Vol. 35, iss. 6. — P. 325-339.
Esipov D.V., Chirkov D.V., Kuranakov D.S., Lapin V.N. Direct numerical simulation of the Segre–Silberberg effect using Immersed boundary method // Journal Fluids Engineering. — 2020. — Vol. 142, iss. 11. — Art No. 111501.
Esipov D.V., Lapin V.N., Kuranakov D.S., Chirkov D.V. Direct numerical simulation of viscous incompressible flow with spherical particles in the flat channel // Journal of Physics: Conference Series. — 2019. — Vol. 1404.
Karnakov P.V., Kuranakov D.S., Lapin V.N., Cherny S.G., Esipov D.V. Peculiarities of the hydraulic fracture propagation caused by pumping of proppant-fluid slurry // Thermophysics and Aeromechanics. — 2018. — Vol. 25, iss. 4. — P. 587-603.
Cherny S., Esipov D., Kuranakov D., Lapin V., Chirkov D., Astrakova A. Prediction of fracture initiation zones on the surface of three-dimensional structure using the surface curvature // Engineering Fracture Mechanics. — 2017. — Vol. 172. — P. 196-214.
Shokin Yu., Cherny S., Lapin V., Esipov D., Kuranakov D., Astrakova A. Methods for optimal control of hydraulic fracturing process // CEUR Workshop Proceedings. — 2017. — Vol. 1839. — P. 423-444.
Cherny S., Lapin V., Esipov D., Kuranakov D., Avdyushenko A., Lyutov A., Karnakov P. Simulating fully 3D non-planar evolution of hydraulic fractures // International Journal of Fracture. — 2016. — Vol. 201 (2). — P. 181-211.
Kuranakov D.S., Esipov D.V., Lapin V.N., Cherny S.G. Modification of the boundary element method for computation of three-dimensional fields of strain-stress state of cavities with cracks // Engineering Fracture Mechanics. — 2016. — Vol. 153. — P. 302-318.
Shokin Yu., Cherny S., Esipov D., Lapin V., Lyutov A., Kuranakov D. Three-dimensional model of fracture propagation from the cavity caused by quasi-static load or viscous fluid pumping // Communications in Computer and Information Science. — 2015. — Vol. 549. — P. 143-157.
Alekseenko O.P., Potapenko D.I., Cherny S.G., Esipov D.V., Kuranakov D.S., Lapin V.N. 3D Modeling of fracture initiation from perforated non-cemented well-bore // SPE Journal — 2013. — Vol. 18, No. 3. — P. 589-600.
Bannikov D.V., Esipov D.V., Cherny S.G., Chirkov D.V. Optimization design according to the efficiency-strength criteria // Thermophysics and Aeromechanics. — 2010. — Vol. 17., Iss. 4. — P. 613-620.
Blokhin A.M., Tkachev D.L., Esipov D.V. Well-posedness of a modified initial-boundary value problem on stability of shock waves in a viscous gas. Part II // Journal of Mathematical Analysis and Applications. — 2007. — Vol. 331, iss. 1. — P. 424-442.


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.

My Experiences

Vice director for research 2016 Oct - 2021 Feb

Federal Research Center for Information and Computational Technologies

Academic secretary 2014 Feb - 2016 Oct

Institute of Computational Technologies, SB RAS

Senior researcher 2014 Feb - 2021 Feb

Laboratory of mathematical modeling (Head of the laboratory is prof. Sergey Cherny), Institute of Computational Technologies, SB RAS

Researcher 2012 Nov - 2014 Jan

Laboratory of mathematical modeling (Head of the laboratory is prof. Sergey Cherny), Institute of Computational Technologies, SB RAS

Teacher assistant 2013 Jul - 2018 Jun

Chair of Mathematical Modelling, Novosibirsk State University

My Education

Phd in Mathematical modelling, numerical methods and software 2007 Sep - 2012 Feb

The PhD thesis "Simulation of initiation and propagation processes for hydraulic fractures" was defended in dissertation сouncil DM 003.046.01

Master of Mathematics 2001 Sep - 2007 Jun

Novosibirs State University, Mechanical and Mathematical Faculty

Look deep into nature, and then you will understand everything better.

Albert Einstein


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 ODE. 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) 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 5251. To make a first impression on the boundary element methods, I recommend looking into Wikipedia.
Here is a preliminary version of the book "Problem book in Numerical methods" (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.

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.