Constrained Interpolation Profile Scheme Research Articles

Axisymmetric Electromagnetic Wave Propagation Computation Using the Constrained Interpolation Profile Scheme With Large Time Steps

Conventional explicit time-domain methods used to solve Maxwell's equations are reliable and robust but are conditionally stable and often require the fulfillment of the condition Courant-Friedrichs-Lewy (CFL) ≤ 1. While this is acceptable for many applications, in some instances, where Maxwell's equations are solved alongside systems with slower propagation velocities, explicit methods prove costly. This is the case for nonrelativistic electromagnetic Particle-In-Cell methods that are required to study plasma thrusters. Several algorithms have been proposed to retain a nearly explicit formulation using large time steps to achieve higher CFL values. Among these is the semi-Lagrangian constrained interpolation profile (CIP) method. While the ability of this method to handle CFL > 1 has been demonstrated for planar 2-D-3-D cases, this has not been done for 2-D cases with cylindrical symmetry. In this article, a procedure is presented to compute the electromagnetic wave propagation in 2-D domains with cylindrical symmetry using the CIP method. The CIP scheme is extended for CFL ≥ 1 cases, and a ghost node method is proposed to deal with the axis singularity and with the wall boundary condition. The results are compared with the fields of a Hertzian dipole and with a coaxial cable, and they show a good agreement.

Animating turbulent fluid with a robust and efficient high‐order advection method

AbstractThe accuracy of advection has a great influence on the visual effect of fluid simulation. Constrained interpolation profile (CIP) method has been an important advection scheme because of its third‐order accuracy and the fact that it only needs to be performed over a compact stencil, but extending it to high‐dimensional advection equations is not easy, because it involves complex calculations and large memory overheads, and is usually unstable. In this article, we propose a stable and efficient three‐dimensional (3D) CIP scheme which can maintain high accuracy but requires low computation and memory cost. We first construct an efficient two‐dimensional (2D) CIP scheme based on dimensional splitting and local Taylor expansions, and then propose an effective way to extend it for 3D applications without decreasing the computational accuracy or affecting the stability. The experimental results show the advantages of our method over the state‐of‐the‐art advection schemes.

Numerical Modelling of Interaction between Solitary Wave and Sloped Seawall

A numerical model for solving interaction between solitary wave and a sloped seawall is established. The CIP (Constrained Interpolation profile) scheme is employed to solve the flow field. THINC (Tangent of Hyperbola Interpolation for Interface Capturing) method is applied for capturing the free surface. Hydrodynamic forces is calculated by integrating the pressure and friction along the seawall surface. First, convergence tests with respect to mesh resolution and time step are examined, and the solitary wave profile is validated by experimental data from the published paper. Then, time series of the free surface elevation at specific location with different heights of incident solitary wave are presented. Finally, hydrodynamic forces acting on the weather side of the seawall are analyzed. The conclusion can be drawn that this numerical model has applicability for strongly nonlinear wave-body interaction problems.

Numerical Simulation of Water Entry of Wedges Based on the CIP Method

The hydrodynamic problems for water entry of wedges are studied by a constrained interpolation profile (CIP) based on Cartesian grid method. The CIP scheme was applied to the Cartesian grid based on flow solver, which was first described. The tangent of hyperbola for interface capturing (THINC) scheme was applied to capture the free surface. The CIP method was extended to capture the dynamics in the water entry approach. The simulations were performed in three aspects. First, pressure distributions for the wedges entering into water with constant speed were predicted, and the results were compared with the similarity solutions by the boundary element method (BEM). Then simulations were conducted for the free-falling wedges entering into water with one degree of freedom. The results were compared with the published experimental data. Finally, the impact of a wedge on the water surface in a free fall motion with an initial heel angle was studied. The motion of the wedge was subjected to three degrees of freedom, and the results were also compared with those of experiments.

Application of the Constrained Interpolation Profile (CIP) scheme to two-dimensional single-phase hydrothermal reservoir simulations

The Constrained Interpolation Profile (CIP) scheme is applied to two-dimensional single-phase numerical simulations of hydrothermal reservoirs for effectively controlling numerical dispersion. The advection terms of the equations for the conservation of mass, enthalpy, and a tracer are solved using the CIP scheme and the non-advection terms, using the finite difference method. The CIP scheme successfully reproduces the high-contrast temperature distribution during cold water reinjection into a hydrothermal reservoir. The flow of a tracer injected into the same reservoir with little dilution is also simulated successfully. In both problems, the conventional first-order upstream difference scheme suffers from severe numerical dispersion.

Effective hydrodynamic hydrogen escape from an early Earth atmosphere inferred from high-accuracy numerical simulation

Hydrodynamic escape of hydrogen driven by solar extreme ultraviolet (EUV) radiation heating is numerically simulated by using the constrained interpolation profile scheme, a high-accuracy scheme for solving the one-dimensional advection equation. For a wide range of hydrogen number densities at the lower boundary and solar EUV fluxes, more than half of EUV heating energy is converted to mechanical energy of the escaping hydrogen. Less energy is lost by downward thermal conduction even giving low temperature for the atmospheric base. This result differs from a previous numerical simulation study that yielded much lower escape rates by employing another scheme in which relatively strong numerical diffusion is implemented. Because the solar EUV heating effectively induces hydrogen escape, the hydrogen mixing ratio was likely to have remained lower than 1vol% in the anoxic Earth atmosphere during the Archean era.

3-D numerical simulations of violent sloshing by CIP-based method

The violent sloshing flow inside a rectangular tank is computed by the CIP (Constrained Interpolation Profile)[1] based Cartesian grid method. Two kinds of CIP scheme, the original CIP scheme and the RCIP scheme, have been applied to the flow solver. 2-D and 3-D computations using the two CIP schemes are carried out and their performances are discussed by comparing the results of the impact pressures on the wall and the free surface profiles to the experimental measurements.

A Nearly Perfect Total-Field/Scattered-Field Boundary for the One-Dimensional CIP Method

A total-field/scattered-field (TF/SF) boundary which is commonly used in the finite-difference time-domain (FDTD) method to illuminate scatterers by plane waves, is developed for use in the constrained interpolation profile (CIP) method. By taking the numerical dispersion into account, the nearly perfect TF/SF boundary can be achieved, which allows us to calculate incident fields containing high frequency components without fictitious scattered fields. First of all, we formulate the TF/SF boundary in the CIP scheme. The numerical dispersion relation is then reviewed. Finally the numerical dispersion is implemented in the TF/SF boundary to estimate deformed incident fields. The performance of the nearly perfect TF/SF boundary is examined by measuring leaked fields in the SF region, and the proposed method drastically diminish the leakage compared with the simple TF/SF boundary.

Two-dimensional numerical simulation and experiment on strongly nonlinear wave–body interactions

A constrained interpolation profile (CIP)-based Cartesian grid method for strongly nonlinear wave–body interaction problems is presented and validated by a newly designed experiment, which is performed in a two-dimensional wave channel. In the experiment, a floating body that has a rectangular section shape is used. A superstructure is installed on the deck and a small floating-body freeboard is adopted in order to easily obtain water-on-deck phenomena. A forced oscillation test in heave and a wave–body interaction test are carried out. The numerical simulation is performed by the CIP-based Cartesian grid method, which is described in this paper. The CIP scheme is applied in the Cartesian grid-based flow solver. New improvements of the method include an interface-capturing method that applies the tangent of hyperbola for interface capturing (THINC) scheme and a virtual particle method for the floating body. The efficiency of the THINC scheme is shown by a dam-breaking computation. Numerical simulations on the experimental problem for both the forced oscillation test and the wave–body interaction test are carried out, and the results are compared to the measurements. All of the comparisons are reasonably good. It is shown, based on the numerical examples, that the present CIP-based Cartesian grid method is an accurate and efficient method for predicting strongly nonlinear wave–body interactions.

Cubic interpolated propagation scheme in numerical analysis of lightwave and optical force

A novel technique using a cubic interpolated propagation or constrained interpolation profile (CIP) scheme for numerical analysis of light propagation in dielectric media is proposed. One- and two-dimensional calculations of the propagation of short Gaussian pulses are performed. The validity of the proposed technique is confirmed by applying it to the examination of the reflection from dielectric media. Using the CIP scheme, the optical force acted upon a dielectric disc is also calculated and it is shown that the direction of the calculated force is consistent with the direction predicted from theory.

Application of CIP Method for Strongly Nonlinear Marine Hydrodynamics

A CFD approach based on the CIP (Constrained Interpolation Profile) method has been developed for predicting strongly nonlinear marine hydrodynamics. The numerical model uses a Cartesian grid for numerical solution and applies the CIP method for the flow solver and the free-surface interface capturing. An efficient interface capturing method by using a conservative CIP scheme is applied to two-dimensional sloshing. For strongly nonlinear wave-body interactions, a Cartesian grid method, in which the body surface is approximated by distributing virtual particles on it, treats the boundary condition at the body surface. A three-dimensional numerical simulation on a ship moving in large waves is presented.

Development of CIP-Reversed Weighted Residual Method for Water Flow with Free Water Surface and Arbitrary Topography (Algorithmic Improvements and Applications)

A new numerical method for solving a flow with a free water surface and an arbitrary topography is described. The method is based on the constrained interpolation profile (CIP) scheme and the finite-element method (FEM). Although advection terms are accurately solved using the conventional CIP scheme, nonadvection terms are solved by FEM. To solve nonadvection terms, the reversed weighted residual method (RWRM) based on FEM is proposed. Using the RWRM, surface boundary conditions can be imposed on an arbitrarily curved water surface appropriately even if a simple Cartesian mesh system is employed and the surface is not fitted to the boundaries of a computational mesh. Furthermore, in this paper, an algorithmic improvement in the pressure acceleration phase is proposed. By using the improved numerical procedure, the computational cost due to a matrix-solution can be reduced efficiently. The improved CIP-RWRM solver is applied to 2-D solutions to examine its efficiency and accuracy. The computational results show good agreements with the results calculated by other numerical methods for a multiphase flow.

Exactly Conservative Semi-Lagrangian Scheme for Multi-dimensional Hyperbolic Equations with Directional Splitting Technique

A new numerical method that guarantees exact mass conservation is proposed to solve multidimensional hyperbolic equations in semi-Lagrangian form. The method is based on the constrained interpolation profile (CIP) scheme and keeps the many good characteristics of the original CIP scheme. The CIP strategy is applied to the integral form of variables. Although the advection and nonadvection terms are separately treated, mass conservation is kept in the form of a spatial profile inside a grid cell. Therefore, it retains various advantages of the semi-Lagrangian solution with exact conservation, which has been beyond the capability of conventional semi-Lagrangian schemes.