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These equations admit complicated wave solutions, which poses numerical challenges.
The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to self-sharpening and its sharp corner solutions.
Implementation of boundary conditions in cardiovascular simulations poses numerical challenges due to the complex dynamic behavior of the circulatory system.
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Devices composed of rigid bodies interacting through frictional contacts and mechanical joints pose numerical solution challenges because of the discontinuous nature of the motion.
In general, computation of a Pareto-optimal equilibrium point in mixed strategies of a finite game poses a numerical challenge for the following reason.
Next, we overcome the formidable numerical challenges posed by the model by designing a robust semi-implicit method based on linear asymptotic behavior of the leading order terms at small scales, by exploiting the exponential structure of global (integral) operators, and by parallelizing the non-linear optimization problem.
The numerical challenge posed in a shock situation is that high-order finite difference schemes lead to significant oscillations in the vicinity of shocks despite that such schemes result in higher accuracy in smooth regions.
An accurate treatment of material interfaces in compressible multiphase flows poses important challenges for high-resolution numerical methods.
The evolution of high-speed initially laminar multicomponent flows into a turbulent multi-material mixing entity, e.g., in the Richtmyer Meshkov instability, poses significant challenges for high-fidelity numerical simulations.
Because of its complex nature, cavitation associated with marine propellers poses a challenge to numerical simulations for predicting it.
Establishing a set of physically-rational and meanwhile computationally-maneuverable boundary conditions for the tornado-building interaction scenario poses a challenge to numerical simulation developers.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com