An enhanced dual IDW method for high-quality geospatial interpolation.
Ontology highlight
ABSTRACT:
SUBMITTER: Li Z
PROVIDER: S-EPMC8110750 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:This paper describes a novel 2nd order direct forcing immersed boundary method designed for simulation of 2D and 3D incompressible flow problems with complex immersed boundaries. In this formulation, each cell cut by the immersed boundary (IB) is reshaped to conform to the shape of the IB. IBs are modeled as a series of 2D planes in 3D space that connect seamlessly at the edges of the cut cells, in a way that mimics conformal grid. IBs are represented in a continuous and consistent fashion from one cell to another, thus eliminating spatial pressure oscillations originating from inconsistent description of the IB as well as the traditional stair-step problem, leading to a more accurate resolution of the boundary layer. Boundary conditions are enforced at the exact location of the IB devoid of interpolation, which guarantees sound simulations even on grids with high aspect ratio, and enables simulations of flow packed with multiple IBs in close proximity. Boundary conditions for each phase across the IB are enforced independently, yielding a unique capability to solve flows with zero-thickness IBs. Simulations of a large number of 2D and 3D test cases confirm the prowess of the devised immersed boundary method in solving flows over multiple loosely/closely-packed IBs; stationary, moving and highly morphing IBs; as well as IBs with zero-thickness. Results show that predictions from the proposed scheme agree remarkably well with theoretical models and experimental data for both integral variables and local flow fields and they are often with less than 1% deviation from solutions obtained by conformal grid of similar resolution.
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Project description:There has been a resurgence of interest in free energy methods motivated by the performance enhancements offered by molecular dynamics (MD) software written for specialized hardware, such as graphics processing units (GPUs). In this work, we exploit the properties of a parameter-interpolated thermodynamic integration (PI-TI) method to connect states by their molecular mechanical (MM) parameter values. This pathway is shown to be better behaved for Mg2+ → Ca2+ transformations than traditional linear alchemical pathways (with and without soft-core potentials). The PI-TI method has the practical advantage that no modification of the MD code is required to propagate the dynamics, and unlike with linear alchemical mixing, only one electrostatic evaluation is needed (e.g., single call to particle-mesh Ewald) leading to better performance. In the case of AMBER, this enables all the performance benefits of GPU-acceleration to be realized, in addition to unlocking the full spectrum of features available within the MD software, such as Hamiltonian replica exchange (HREM). The TI derivative evaluation can be accomplished efficiently in a post-processing step by reanalyzing the statistically independent trajectory frames in parallel for high throughput. We also show how one can evaluate the particle mesh Ewald contribution to the TI derivative evaluation without needing to perform two reciprocal space calculations. We apply the PI-TI method with HREM on GPUs in AMBER to predict p Ka values in double stranded RNA molecules and make comparison with experiments. Convergence to under 0.25 units for these systems required 100 ns or more of sampling per window and coupling of windows with HREM. We find that MM charges derived from ab initio QM/MM fragment calculations improve the agreement between calculation and experimental results.
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Project description:The modified point charge plus continuum (mPC) model [Constantin, L. A.; Phys. Rev. B 2019, 99, 085117] solves the important failures of the original counterpart, namely, the divergences when the reduced gradient of the density is large, such as in the tail of the density and in quasi-dimensional density regimes. The mPC allows us to define a modified interaction-strength interpolation (mISI) method inheriting these good features, which are important steps toward the full self-consistent treatment. Here, we provide an assessment of mISI for molecular systems (i.e., considering thermochemistry properties, correlation energies, vertical ionization potentials, and several noncovalent interactions), harmonium atoms, and functional derivatives in the strong-interaction limit. For all our tests, mISI provides a systematic improvement over the original ISI method. Semilocal approximations of the second-order Görling-Levy (GL2) perturbation theory are also considered in the mISI method, showing considerable worsening of the results. Possible further development of mISI is briefly discussed.
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