  There is a pressing demand for robust, high-order baseline schemes for
conservation laws that minimize reliance on supplementary stabilization. In
this work, we respond to this demand by developing new baseline schemes within
a nodal discontinuous Galerkin (DG) framework, utilizing upwind
summation-by-parts (USBP) operators and flux vector splittings. To this end, we
demonstrate the existence of USBP operators on arbitrary grid points and
provide a straightforward procedure for their construction. Our method
encompasses a broader class of USBP operators, not limited to equidistant grid
points. This approach facilitates the development of novel USBP operators on
Legendre--Gauss--Lobatto (LGL) points, which are suited for nodal discontinuous
Galerkin (DG) methods. The resulting DG-USBP operators combine the strengths of
traditional summation-by-parts (SBP) schemes with the benefits of upwind
discretizations, including inherent dissipation mechanisms. Through numerical
experiments, ranging from one-dimensional convergence tests to
multi-dimensional curvilinear and under-resolved flow simulations, we find that
DG-USBP operators, when integrated with flux vector splitting methods, foster
more robust baseline schemes without excessive artificial dissipation.
