This question is a duplicate of Does turning sharply on a bicycle conserve more energy than a wide turn?, but the accepted answer to that question is incorrect, so it's probably safe for now. In general, in the absence of friction, the force of turning applied to something like a bike curving through a turn is approximately perpendicular to the path, and hence does no work.
However, realistically, friction losses will probably play a decent part in it. So, if I were you I'd try setting up the simulation so that $$\frac{dv}{dt}=-\alpha v \frac{d\omega}{dt}$$ or something of the sort, where $\alpha$ is a constant of proportionality which encodes the frictional energy loss associated with turning around the car. This is a model differential equation which states that the speed-damping coefficient is $-\alpha \omega'(t)$, ie, the sharper you turn, the more speed you lose due to friction. Try various values of $\alpha$, and if possible run tests. Which ones look realistic, and which ones look goofy? Testing and debugging to find something which looks "right" is probably the most important part.