Changes between Version 7 and Version 8 of DianaICSolver


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Timestamp:
Sep 13, 2011, 9:41:26 AM (14 years ago)
Author:
miroshkin
Comment:

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  • DianaICSolver

    v7 v8  
    11= Description =
    2 To simulate chemical or biological process in Diana the Initial Value Problem should be solved at first. A guess for initial conditions can be set in model file. [[BR]] Standard {{{ IDACalcIC() }}} method of Sundials package can calculate consistent initial conditions for homogeneous differential algebraic equations systems of the type
    3 
    4 {{{
    5 #!html
    6 <table border="0" width="50%" align="center">
    7 <tr>
    8   <td align = "center" fontsize ="50%" width="90%">
    9   dx<sub>1</sub>/dt = f<sub>1</sub>(x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>, t)<br>
    10   dx<sub>2</sub>/dt = f<sub>2</sub>(x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>, t)<br>
    11              ...            <br>
    12   dx<sub>n</sub>/dt = f<sub>n</sub>(x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>, t)
    13   </td>
    14   <td align="center">(1)
    15   </td>
    16 </tr>
    17 </table>
    18 }}}
    19 
    20 But in case of non-homogeneous differential algebraic equations systems of the type
    21 
    22 {{{
    23 #!html
    24 <table border="0" width="50%" align="center">
    25 <tr>
    26   <td align = "center" fontsize ="50%" width="90%">
    27   F<sub>1</sub>(dx<sub>1</sub>/dt, dx<sub>2</sub>/dt, ..., dx<sub>n</sub>/dt) = f<sub>1</sub>(x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>, t)<br>
    28   F<sub>2</sub>(dx<sub>1</sub>/dt, dx<sub>2</sub>/dt, ..., dx<sub>n</sub>/dt) = f<sub>2</sub>(x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>, t)<br>
    29              ...            <br>
    30   F<sub>n</sub>(dx<sub>1</sub>/dt, dx<sub>2</sub>/dt, ..., dx<sub>n</sub>/dt) = f<sub>n</sub>(x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>, t)
    31   </td>
    32   <td align="center">(2)
    33   </td>
    34 </tr>
    35 </table>
    36 }}}
    37 
    38 {{{IDACalcIC()}}} generates the exception
     2To simulate chemical or biological process in Diana the Initial Value Problem should be solved at first. A guess for initial conditions can be set in model file. [[BR]] Standard {{{ IDACalcIC() }}} method of Sundials package can calculate consistent initial conditions for differential algebraic equations systems, [[BR]]whose state vector can be separated into a dynamic part and algebraic part. If this is not possible {{{IDACalcIC()}}} generates the exception
    393{{{
    404   ECapeUnknown in IDASolver (Diana) startIntegrator, IDACalcIC failed
    415}}}
    426
    43 Consistent initial conditions for differential algebraic equations system  of type (2) can be found with {{{IDACalcIC()}}} method, but the system should be manually changed to form (1) before.[[BR]]
    44 '''''ICSolver''''' can calculate initial conditions for systems of the type (2) without any conversions of the system.
     7'''''ICSolver''''' can calculate initial conditions for systems without any conversions of the equations.
    458
    469= Example =
    4710
    48 [attachment:AdsColumn.mdl "Adsorption column model"] contains the equations system of type (2) example[[BR]]
     11[attachment:AdsColumn.mdl "Adsorption column model"] contains the equations system[[BR]]
    4912[attachment:AdsColumn_error.py "Python script with calling standard IDACalcIC() method"] generates the exception[[BR]]
    5013[attachment:AdsColumn.py "Python script with using ICSolver and nonzero output verbosity level"] shows the initial state vector and message