Related papers: Highly efficient exponential scalar auxiliary vari…
This paper introduces a novel paradigm for constructing linearly implicit and high-order unconditionally energy-stable schemes for general gradient flows, utilizing the scalar auxiliary variable (SAV) approach and the additive Runge-Kutta…
We construct new first- and second-order pressure correction schemes using the scalar auxiliary variable (SAV) approach for the Navier-Stokes equations. These schemes are linear, decoupled and only require a sequence of solving Poisson type…
We present a novel optimization algorithm, element-wise relaxed scalar auxiliary variable (E-RSAV), that satisfies an unconditional energy dissipation law and exhibits improved alignment between the modified and the original energy. Our…
We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the SAV approach combined with the Lagrangian multiplier approach. They are as efficient…
We introduce novel entropy-dissipative numerical schemes for a class of kinetic equations, leveraging the recently introduced scalar auxiliary variable (SAV) approach. Both first and second order schemes are constructed. Since the…
The kinetic Langevin dynamics finds diverse applications in various disciplines such as molecular dynamics and Hamiltonian Monte Carlo sampling. In this paper, a novel splitting scalar auxiliary variable (SSAV) scheme is proposed for the…
It is well-known that the Allen-Cahn equation not only satisfies the energy dissipation law but also possesses the maximum bound principle (MBP) in the sense that the absolute value of its solution is pointwise bounded for all time by some…
In this paper, two efficient and magnetization norm preserving numerical schemes based on the scalar auxiliary variable (SAV) method are developed for calculating the ground state in micromagnetic structures. The first SAV scheme is based…
For a class of fourth order gradient flow problems, integration of the scalar auxiliary variable (SAV) time discretization with the penalty-free discontinuous Galerkin (DG) spatial discretization leads to SAV-DG schemes. These schemes are…
A novel numerical strategy is introduced for computing approximations of solutions to a Cahn-Hilliard model with degenerate mobilities. This model has recently been introduced as a second-order phase-field approximation for surface…
In this paper, we present a novel strategy to systematically construct linearly implicit energy-preserving schemes with arbitrary order of accuracy for Hamiltonian PDEs. Such novel strategy is based on the newly developed exponential scalar…
In this paper we propose and analyze a second order accurate (in time) numerical scheme for the square phase field crystal (SPFC) equation, a gradient flow modeling crystal dynamics at the atomic scale in space but on diffusive scales in…
In this paper, we present a novel semi-implicit numerical scheme for the stochastic Cahn--Hilliard equation driven by multiplicative noise. By reformulating the original equation into an equivalent stochastic scalar auxiliary variable…
This paper develops a generalized scalar auxiliary variable (SAV) method for the time-dependent Ginzburg-Landau equations. The backward Euler is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.…
In this paper, we propose a novel Lagrange Multiplier approach, named zero-factor (ZF) approach to solve a series of gradient flow problems. The numerical schemes based on the new algorithm are unconditionally energy stable with the…
In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state (e.g. Peng-Robinson equation of state). The methods are…
We consider a kind of differential equations d/dt y(t) = R(y(t))y(t) + f(y(t)) with energy conservation. Such conservative models appear for instance in quantum physics, engineering and molecular dynamics. A new class of energy-preserving…
The paper studies a scalar auxiliary variable (SAV) method to solve the Cahn-Hilliard equation with degenerate mobility posed on a smooth closed surface {\Gamma}. The SAV formulation is combined with adaptive time stepping and a…
In this paper, we propose and analyze an efficient implicit--explicit (IMEX) second order in time backward differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems using the scalar auxiliary variable…
We present a systematical approach to developing arbitrarily high order, unconditionally energy stable numerical schemes for thermodynamically consistent gradient flow models that satisfy energy dissipation laws. Utilizing the energy…