Sand dunes are found in a variety of shapes in deserts and coasts and also on the planet Mars. The basic mechanisms of dune formation could be incorporated into a continuum saltation model, which successfully reproduced the shape of the barchan dunes and has been also applied to calculate interaction of barchans in a field. We have recently extended our dune model to investigate other dune shapes observed in nature. Here, we present the first numerical simulation of the transformation of barchan dunes, under the influence of vegetation, into parabolic dunes, which appear frequently on coasts. Further, we apply our model to reproduce the shape of barchan dunes observed on Mars, and we find that an interesting property related to the martian saltation is relevant to predict the scale of dunes on Mars. Our model can also reproduce unusual dune shapes of the Martian north polar region, like rounded barchans and elongated linear dunes. Our results support the hypothesis that these dunes are indurated.