Cell-vertex entropy-stable finite volume methods for the system of Euler equations on unstructured grids

An alternative cell-vertex entropy-stable finite volume method for the system of Euler equations is presented. It is derived from the residual distribution method, using the signals from each triangular element as a foundation for controlling entropy. Each signal has an entropy-conserved and entropy-stable components. From a median dual area perspective, these signals can be interpreted as a line integral of the fluxes along the control volume boundaries of the cell-vertex approach. The new method includes a first-order version which is positive together with a linearity-preserving second order approach. A second order limited version is also presented using entropy as the guiding principle for limiting. Results herein demonstrate that the new method is more accurate and robust relative to the current cell-vertex entropy-stable finite volume method.