In the present study, a conservative overset mesh scheme is proposed for the accurate and robust numerical simulation of unsteady time-accurate flows around multiple objects in relative motion on unstructured meshes. In this approach, blank region is constructed between the overlapping mesh blocks after hole cutting, and this region is refilled with new triangular or tetrahedral elements by interconnecting the vertices between the intergrid boundaries for two or three dimensional flow simulations, respectively. Thus, the multiple overlapping mesh blocks are converted instantaneously into a single-block unstructured mesh. By doing this, the non-conservative interpolation procedure between mesh blocks typically adopted for conventional overset mesh schemes can be avoided, and the conservation principle of mass, momentum and energy fluxes across the overset mesh block boundary is automatically satisfied. For this purpose, an intergrid boundary reconnection technique was developed to enhance the efficiency and the robustness of constructing the blank region and the interconnecting the mesh blocks with new elements.
To validate the capability of the present conservative overset mesh scheme, several numerical experiments were conducted, and the results were assessed against the conventional non-conservative overset mesh scheme and the single-block mesh calculation. It was found that the present conservative overset mesh scheme maintains second-order spatial accuracy well, and the error level is consistently lower than that of the conventional non-conservative scheme. The present conservative scheme is capable of transferring the shock wave across the overset mesh block boundary, similar to the single-block mesh calculation, while the calculation by the non-conservative scheme is prone to numerical difficulties. It was also found that the present conservative overset mesh scheme is consistently less diffusive, and produces minimal spurious mass, similar amount to that of the single-block mesh calculation, compared to the conventional non-conservative scheme. In the case of the flow involving massive flow separation and wake dynamics, the present conservative scheme behaved very similar to the single-block mesh calculation, showing less degree of numerical dissipation and interference across the intergrid boundary than the conventional non-conservative scheme. In spite of the additional computational overhead for the treatment of the intergrid boundary, the calculation by the present conservative scheme converged faster, and the overall computational time required was smaller than the conventional non-conservative scheme. The present conservative overset mesh scheme was also implemented to the three dimensional flow calculations. For incompressible flow calculation, the present conservative scheme is less diffusive, and suppresses the non-physical numerical oscillation effectively by maintaining the conservation of mass. In addition, for compressible flow calculations, the present conservative scheme provides more accurate and robust numerical solution compared to the conventional non-conservative overset mesh scheme, showing similar numerical behavior to the two dimensional flow simulations.
From these numerical investigations, it was concluded that the present conservative overset mesh scheme coupled with the intergrid boundary reconnection technique is more accurate, efficient, and robust for the simulation of unsteady flows involving multiple objects in relative motion, compared to the conventional non-conservative overset mesh scheme.
