A high-order compact finite difference scheme and precise integration method based on modified Hopf-Cole transformation for numerical simulation of \(n\)-dimensional Burgers’ system. (English) Zbl 1433.65156
Summary: This paper modifies an \(n\)-dimensional Hopf-Cole transformation to the \(n\)-dimensional Burgers’ system. We obtain the \(n\)-dimensional heat conduction equation through the modification of the Hopf-Cole transformation. Then, the fourth-order precise integration method (PIM) in combination with a spatially global sixth-order compact finite difference (CFD) scheme is presented to solve the equation with high accuracy. Moreover, coupling with the Strang splitting method, the scheme is extended to multi-dimensional (two, three-dimensional) Burgers’ system. Numerical results show that the proposed method appreciably improves the computational accuracy compared with the existing numerical method. Moreover, the two-dimensional and three-dimensional examples demonstrate excellent adaptability, and the numerical simulation results also have very high accuracy in medium Reynolds numbers.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
\(n\)-dimensional Hopf-Cole transformation; \(n\)-dimensional Burges’ system; compact finite difference; precise integration method; Strang splitting methodSoftware:
PFQReferences:
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