View source for Lid driven cavity

{{Box-round|title= Related papers |
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/29512743.pdf G. Kosec; A local numerical solution of a fluid-flow problem on an irregular domain, Advances in engineering software, vol. 120, 2018 [DOI: 10.1016/j.advengsoft.2016.05.010]]
}}

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=Intro=

Let's try MLSM and described solution procedures first  on a lid driven cavity problem that stands for a standard benchmark test for validation of the fluid flow solvers. It has been proposed in 1982  and since then solved by many researchers with wide spectra of different numerical methods. The test is still widely studied and used for validation of novel methods and numerical principles. Case is schematically presented in <xr id="fig:lid_driven_scheme"/> followed by few basic analyses, just to show that things work as they should. Details about comparison can be found in [http://comms.ijs.si/~gkosec/data/papers/29512743.pdf paper]
 
<figure id="fig:lid_driven_scheme">
[[File:FF_.png|400px]]
<caption>Scheme of a lid driven cavity case</caption>
</figure>

=Code=
The snippet of the MLSM code for an explicit ACM method with CBS looks like: (full examples, including '''implicit versions''', can be found under the examples in the [https://gitlab.com/e62Lab/medusa code repository]).
<syntaxhighlight lang="c++" line>
    for (int step = 0; step <=O.t_steps; ++step) {
        // Navier-Stokes
        for (auto c:interior) 
            // Navier-Stokes
            v2[c] = v1[c] + O.dt * ( - 1/O.rho    * op.grad(P1,c)
                                     + O.mu/O.rho * op.lap(v1, c)
                                     -              op.grad(v1,c)*v1[c]);
        }
        // Mass continuity
        for (auto i:interior) { 
            P2[i] = P1[i] - O.dl * O.dt * O.rho * op.div(v2,i) + O.dl2 * O.dl * O.dt * O.dt * op.lap(P1,i);
        }
        v1.swap(v2);
        P1.swap(P2);
    }
</syntaxhighlight>

=Results=

[[File:lid_driven_contour_Re3200.png|600px]][[File:lid_driven_contour_Re100.png|600px]]


[[File:lid_driven_explicit_exec_time.png|600px]][[File:lid_driven_explicit_convergence.png|600px]]


<figure id="fig:lid_driven_comparison">
[[File:lid_driven_comparison.png|600px]]
<caption>Cross section  velocity profiles.</caption>
</figure>