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Efficient Entropy-Stable Discontinuous Spectral-Element Methods Using Tensor-Product Summation-by-Parts Operators on Triangles and Tetrahedra
Tristan Montoya, David W. Zingg
We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular…
Quadrature Rules on Triangles and Tetrahedra for Multidimensional Summation-By-Parts Operators
Zelalem Arega Worku, Jason E. Hicken, David W. Zingg
Multidimensional diagonal-norm summation-by-parts (SBP) operators with collocated volume and facet nodes, known as diagonal- operators, are attractive for entropy-sta…
Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra
Tristan Montoya, David W. Zingg
We present an extension of the summation-by-parts (SBP) framework to tensor-product spectral-element operators in collapsed coordinates. The proposed approach enables the construct…
Entropy-split multidimensional summation-by-parts discretization of the Euler and compressible Navier-Stokes equations
Zelalem Arega Worku, David W. Zingg
High-order Hadamard-form entropy stable multidimensional summation-by-parts discretizations of the Euler and compressible Navier-Stokes equations are considerably more expensive th…