[SmileMax]

If you use OpenFOAM's built-in random number class, you can use the functions prefixed with global to ensure that the random numbers generated each time are kept in sync on all MPI nodes，such as Random::globalSample01(), Random::globalGaussNormal().

see src/OpenFOAM/primitives/random/Random/Random.C for these source codes:

Foam::scalar Foam::Random::globalSample01()
{
    scalar value(-GREAT);
 
    if (Pstream::master())
    {
        value = scalar01(); // generate random number on master MPI node.
    }
    Pstream::scatter(value); // broadcast this value to all MPI nodes.
    return value;
}

But in fact, the random numbers obtained by the built-in functions of OpenFOAM are always the same on different MPI nodes and even in different running stages if you give a fixed random seed. You can use Pout to output the value of each node to observe this phenomenon:

Random rndGen(<a fixed random seed>);

scalar a = rndGen.sample01<scalar>();
Pout << "random number: "<< a << endl;

scalar b = rndGen.globalSample01<scalar>();
Pout << "random number: "<< b << endl;

// a is always equal to b here, and each MPI node have the same value of a and b.

If you are using an external random number class, such as std:rand, You can refer to the implementation method of Random::globalSample01 above to manually complete random number synchronization between MPI nodes.