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At the same time, the compact scheme can capture strong shocks as well.
The consistency of mass flux across the normal shock is needed for a Riemann solver to capture strong shocks stably.
The proposed method is designed primarily to capture strong nonlinear behavior and may be applied to model reduction, nonlinear characterization and control design.
Numerical experiments show its capacity to preserve the accuracy of discontinuous Galerkin method in smooth regions, and to capture strong shocks.
Through systematic test and comparison with the regular WENO schemes, we observe that the nonlinear weighted compact schemes have the same ability to capture strong discontinuities, while the resolution of short waves is improved and numerical dissipation is reduced.
Through systematic analysis and numerical tests, we show that our nonlinear compact scheme has high order, high resolution and low dissipation, and has the same ability to capture strong discontinuities as regular weighted essentially non-oscillatory (WENO) schemes.
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It aims to look beyond today's incremental improvements "to create a shared sense of direction, to spark a wave of innovation and to move the plastics value chain into a positive spiral of value capture, stronger economics, and better environmental outcomes".
The report concludes that it is vital "to overcome the limitations of today's incremental improvements and fragmented initiatives, to create a shared sense of direction, to spark a wave of innovation and to move the plastics value chain into a positive spiral of value capture, stronger economics, and better environmental outcomes".
A high-speed flow test case is used to demonstrate the ability of the hp-refinement approach for capturing strong shocks or discontinuities while improving functional accuracy.
Calcium manganese oxides have captured strong scientific interest in recent years due to exceptional catalytic activities, inexpensive synthesis methods, and constitution of earth abundant and environmentally benign elements.
Both classes of numerical schemes are quite successful for advection equations capturing strong gradients or even discontinuities, because they allow their approximate solutions to be discontinuous at the grid cell interfaces.
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CEO of Professional Science Editing for Scientists @ prosciediting.com