The answer to your question is yes.
As you say, laminar, non-compressible flow can be neatly represented by very elegant mathematical models. Flows around even complicated shapes can be modelled using the different models like building blocks - very satisfying mathematics, and probably fair to give credit to Soviet aerodynamicists as they were absolute masters at it.
These neat models do not work for compressible or turbulent flow. To model these sorts of flows, "finite element analysis" is used. Basically the entire flow field is divided into an imaginary mesh of cells ("elements"). If these cells are small enough, the flow within that cell can be represented by simple mathematical models (temperature, density, velocity are assumed constant in the cell). Thermodynamic and mechanical theory are then used to predict the characteristics of the flow in the neighbouring cell.
This model only works if the key assumption of uniform density and velocity is accurate. And that is only the case if the cells are small enough. The smaller cells you have, the bigger computer you need. The need for powerful computers is probably why US aerodynamicists started to overtake the Soviets in the 1970s and 1980s. The computing power needed today is enormous - most of the world's biggest computers are chugging away on finite element analysis of one sort or another - whether predicting weather patterns, or the flow around a gas-turbine blade, or the wing of an F1 car.