modeling tool for stiff heterogeneous systems

Modeling Tool for Stiff Heterogeneous Modeling Tool for Stiff Heterogeneous SystemsSystems

Yury Shornikov1, Eugeny Novikov2

1 Design Technological Institute of Digital Techniques SB RAS,Novosibirsk, Russia, shornikov@inbox.ru

2 Institute of Computational Modeling SB RAS,Krasnoyarsk, Russia, novikov@icm.krasn.ru

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Class of SystemsClass of Systems

;

;

Discrete-continuous systems. For example, the constrained pendulum.

Classes of HS Continuous BehaviorClasses of HS Continuous Behavior

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Systems Models of Continuous Modes

Electromechanical ODE

Automation ODE having retarded arguments

Chemical kinetics ODE

Biological ODE, PDE

Electrical DAE

Chemical-engineering PDE

Mechanical PDE

Others ODE, DAE, PDE

4

Class of SystemsClass of Systems

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Traction Electric DriveTraction Electric Drive

Block diagram of traction electric drive of electric loader

Structural specification (visual model)

Data ImportData Import

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Changing of the motor torque in time

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Solving Direct Problems of Solving Direct Problems of Chemical KineticsChemical Kinetics

s

N

1iiij

N

1i

k

iij N,1j,ccrr j

ri N,1i,c – reactants

sj N,1j,k – rate constants of stages

αij и βij – stoichiometric coefficients

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Unification of ISMA SoftwareUnification of ISMA Software::Integrated PreprocessorIntegrated Preprocessor

LISMALISMA GG

;S S

C SC S

S E aE

ida

cidO

T*OOT

ETTE SS

:LISMAG C

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Ethane PyrolysisEthane Pyrolysis

2 6 3 3

3 2 6 4 2 5

2 5 2 4

2 6 2 2 5

2 5 2 5 4 10

,

,

,

,

.

C H CH CH

CH C H CH C H

C H C H H

H C H H C H

C H C H C H

8,1j,y j - concentrations of reactants

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Biliary SystemBiliary System

Reception Ejection

 Daily bile secretion

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Biliary SystemBiliary SystemOutput intensity of the bile in 12

duodenum Output intensity of the bile into

the bile duct

Mode «reception»

Mode «ejection»

Class of SystemsClass of SystemsSystem of differential-algebraic equations (DAE) with constraints:

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0 0 0 0 0

, , ,

, , ,

: , , 0,

, , , ,

where , , ,

: ,

: ,

: .

yx

y yx

yx

yx

k

NN

N NN

NN Nx

NN S

y f x y t

x x y t

pr g x y t

t t t x t x y t y

x R y R t R

f R R R R

R R R R

g R R R R

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Ring Modulator*Ring Modulator*

*Kampowski W., Rentrop P., Schmidt W. Classication and numerical simulation of electric circuits // Surveys on Mathematics for Industry, 2(1):23 65, 1992

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Ring Modulator:Ring Modulator:Program Model in ISMAProgram Model in ISMA

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Practical Modeling of HSPractical Modeling of HSRing modulator: comparative evaluation

Characteristics ISMAMK22*

DLSODE

MVS AnyLogic

Simulink

Number of computing the right side

474213 496073 _ _ _

Number of returns 496073 16946 _ _ _

*Novikov А.Е., Novikov Е.А., Shornikov Y.V. Approximation of Jacobi matrix in (2,2)-method of solving hybrid systems // Report of Academy of Science of Higher School of Russian Federation, 2008, #1(10). – P. 31-44.

Original Explicit, Semi-Explicit and Adaptive Integration Original Explicit, Semi-Explicit and Adaptive Integration Algorithms in the ISMAAlgorithms in the ISMA**

* Instrumental tools of computerized analysis (ISMA) / Yu.V. Shornikov, V.S. Druzhinin, N.А. Makarov, K.V. Omelchenko, and I.N. Tomilov // Official registration license for computers No. 2005610126, Мoscow, Rospatent, 2005.

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High-Dimensional ModelsHigh-Dimensional ModelsModel of penetration of radioactive labeled antibodies in a tumor affected tissue of a

living oragnism (Akzo Nobel Central Research)

20t0,Ry,g0y,y,tfdt

dy N2

,ykyf

,ykyyy2y

2

yyf

1j2j2j2

j21j221j21j23j2

j3j21j2

j1j2

.v,0,...,v,0,v,0g,Rg

,yy,tty,N

1

,Nj1,c1j,c1j2

T000

N2

1N21N21

24j

23j

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Text Model in ISMAText Model in ISMA

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Dependency of Calculation Time Dependency of Calculation Time From System DimensionFrom System Dimension

Simulation results from:http://www.dm.uniba.it/~testset/report/medakzo.pdf

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Comparison of Solutions Obtained Comparison of Solutions Obtained by Explicit and Implicit Methodsby Explicit and Implicit Methods

RADAU5

RADAU5, RKF78ST

Extending a Class of SystemsExtending a Class of Systems

DAE systems with constraints unresolved for the derivative:

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0 0 0 0 0

, , , 0,

, , ,

: , , 0,

, , , ,

where , , ,

: ,

: ,

: .

yx

y y yx

yx

yx

k

NN

N N NN

NN Nx

NN S

F x y y t

x x y t

pr g x y t

t t t x t x y t y

x R y R t R

F R R R R R

R R R R

g R R R R

Instrumental Simulation of EPSInstrumental Simulation of EPS

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Dostovalov D.N. Program of graphical sheme editor for electro-power systems ISMA EPS (ISMA Electric Power Systems) / Yu.V. Shornikov, A.N. Komarichev, D.N. Dostovalov // Certificate of state registration of computer programs #2013617771. M.:  Federal Service for Intellectual Property. - 2013.

Algorithm for Analysis of Implicit ProblemsAlgorithm for Analysis of Implicit Problems**

• Problem definition:

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* Novikov E.A., Yumatova L.A. A few methods for solving of ordinary differential equations unresolved for the derivative // Reports of the Academy of Sciences of the USSR, vol.295, №4, 1987. – pp.809-812.

0 0 0 0

, 0,

where ,

, .

F x y

y x

x t x y t y

• Numerical scheme:

1 1 1 1 1 1

1 1 1

, ,

,

1( ), ,

where , , , ,

1, 1.

x yn n n n

n ny nx

x y xn ny n n n

nx n n ny n n

x x p k y y p k

D F ahF

D k h F y F k k hyah

F F x y x F F x y y

a p

Event Detection in HSEvent Detection in HS**

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* 1. Novikov E.A., Shornikov Yu.V. Computer simulation of stiff hybrid systems: monograph / Novosibirsk: Publishing house of the NSTU, 2012, 451p. 2. Esposito J., Kumar V., Pappas, G.J.: Accurate event detection for simulating hybrid systems. In: Hybrid Systems: Computation and Control (HSCC). Volume LNCS 2034, Springer–Verlag, 1998.

Event Detection AlgorithmEvent Detection Algorithm

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Test of Event Detection AlgorithmTest of Event Detection Algorithm

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a) – without taking into account the dynamics of an event function, .b) – using the event-detection algorithm, .

Movement

Rebound:

: 0,

.

pr y

v v

Modal behavior:

0,

0.

y v

v a

a b

1 0 75. 2 0 06.

Extending a Class of SystemsExtending a Class of SystemsContinuous behavior of HS is determined by the systems differential-algebraic equations and PDEs.

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2

2

0 0 0 0

0 0

2

, , , , , ,

, ,

: , 0,

, , , ,

, , , ,

,

, , , ,

: ,

: ,

: ,

px z

x x

p px z z

x

k m

p

NN N

N N

N NN N N

N S

z z zx z t p

t p p

x x t

pr g x t

x t p x z t p z

t t t p p p

zz p

n

x R z R t R p R

R R R

R R R R R R

g R R R

Thank you for your attentionThank you for your attention!!

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Yury Shornikov1, Eugeny Novikov2

1 Design Technological Institute of Digital Techniques SB RAS,Novosibirsk, Russia, shornikov@inbox.ru

2 Institute of Computational Modeling SB RAS,Krasnoyarsk, Russia, novikov@icm.krasn.ru