Scalability of OpenFOAM Density-Based Solver with Runge–Kutta Temporal Discretization Scheme

Algorithm 1

The Eulerian fluxes are calculated explicitly so that the ordinary differential equations system can be constructed and further integrated in time by using explicit Runge–Kutta algorithm.

	Result: construct Eulerian fluxes explicitly
	while runTime.loop() do
	Saving quantities at preavious time steps if rk4 then
	/ The following firstly constructs the Eulerian fluxes by applying the Kurganov and Tadmor (KT) scheme. /
	surfaceScalarField phi
	(“phi,”
	());
	surfaceVectorField phiUp
	(“phiUp,”
	(
	+ );
	surfaceScalarField phiEp
	(“phiEp,”
	(
	+
	+ ));
	/ Then, the divergence theorem (Gauss’s law) is applied to relate the spatial integrals to surface integrals.
	/
	volScalarField phiSum (“phiSum,” );
	volVectorField phiUpSum2 (“phiUpSum2,” );
	volVectorField phiUpSum3 (“phiUpSum3,” );
	else
	end
	end