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Implicit dual time-stepping positivity-preserving entropy-stable schemes for the compressible Navier-Stokes equations

We generalize the explicit high-order positivity-preserving entropy-stable spectral collocation schemes developed in [30, 34] for the three-dimensional (3D) compressible Navier Stokes equations to a time implicit formulation. The time derivative …

A surprisingly effective algorithm for the simplification of integrals and sums arising in the partial differential equations and numerical methods

Conservation laws and dissipated quantities are fundamental in analysis. Here we discuss them in partial differential equations and their discretizations. These quantities are integral expressions or, in the discrete case, sums. Often, checking their …