Local mesh refinement features have now been added to a number of numerical ocean
models. In its crudest form, a high-resolution grid is embedded (or nested) in a coarse …

We present a numerical method for solving Poisson's equation, with variable coefficients
and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite …

We introduce Neural Flow Maps, a novel simulation method bridging the emerging
paradigm of implicit neural representations with fluid simulation based on the theory of flow …

In many problems in partial differential equations, one is confronted with problems having
multiple length scales and strong spatial localizations. Examples include nonlinear systems …

An immersed boundary method for the incompressible Navier–Stokes equations in irregular
domains is developed using a local ghost cell approach. This method extends the solution …

We present a new multigrid scheme for solving the Poisson equation with Dirichlet boundary
conditions on a Cartesian grid with irregular domain boundaries. This scheme was …

In many problems in partial differential equations, one is confronted with problems having
multiple length scales and strong spatial localizations. Examples include nonlinear systems …

In the present work we developed a structured adaptive mesh refinement (S-AMR) strategy
for fluid–structure interaction problems in laminar and turbulent incompressible flows. The …

We demonstrate that application of an oscillatory electric field to a liquid yields a long-range
steady field, provided the ions present have unequal mobilities. The main physics is …

We present an algorithm to compute adaptive solutions for incompressible flows using block-
structured local refinement in both space and time. This method uses a projection …