8 papers · 1 filter
Convergence of entropy-stable continuous summation-by-parts discretizations of symmetric hyperbolic conservation laws
Zelalem Arega Worku, David C. Del Rey Fernández, David W. Zingg
The Lax equivalence theorem guarantees convergence of stable and consistent discretizations for linear hyperbolic partial differential equations (PDEs). For nonlinear problems, how…
High-Order Symmetric Positive Interior Quadrature Rules on Two and Three Dimensional Domains
Moustapha Diallo, Zelalem Arega Worku
Fully symmetric positive interior (f-SPI) quadrature rules are key building blocks for high-order discretizations of partial differential equations, yet high-degree rules with few…
Very high-order symmetric positive-interior quadrature rules on triangles and tetrahedra
Zelalem Arega Worku, Jason E. Hicken, David W. Zingg
We present novel fully-symmetric quadrature rules with positive weights and strictly interior nodes of degrees up to 84 on triangles and 40 on tetrahedra. Initial guesses for solvi…
Tensor-Product Split-Simplex Summation-By-Parts Operators
Zelalem Arega Worku, Jason E. Hicken, David W. Zingg
We present an approach to construct efficient sparse summation-by-parts (SBP) operators on triangles and tetrahedra with a tensor-product structure. The operators are constructed b…
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…
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…