user: 请显示与下面列出的汇编代码相匹配的C语言实现:

```asm
<calculate_fg>:
  endbr64
  push   %r15
  push   %r14
  push   %r13
  push   %r12
  push   %rbp
  push   %rbx
  sub    $0x38,%rsp
  mov    %edi,0x34(%rsp)
  mov    %rcx,%rdi
  mov    %esi,0x30(%rsp)
  mov    %rdx,0x8(%rsp)
  mov    %r8,0x10(%rsp)
  mov    %r9,0x18(%rsp)
  movsd  %xmm0,-0x68(%rsp)
  movsd  %xmm1,-0x8(%rsp)
  movsd  %xmm2,(%rsp)
  movsd  %xmm3,-0x18(%rsp)
  movsd  %xmm4,-0x60(%rsp)
  movsd  %xmm5,-0x78(%rsp)
  movsd  %xmm6,-0x10(%rsp)
  test   %esi,%esi
  jle    L55
  mov    0x8(%rsp),%rdx
  movslq 0x34(%rsp),%rax
  mov    0x10(%rsp),%rbx
  mov    (%rdx,%rax,8),%rsi
  mov    (%rdx),%r8
  mov    (%rbx,%rax,8),%rcx
  mov    0x30(%rsp),%eax
  mov    (%rbx),%r9
  lea    0x1(%rax),%edx
  mov    $0x1,%eax
  nopw   0x0(%rax,%rax,1)
L21:
  movsd  (%r8,%rax,8),%xmm0
  movsd  %xmm0,(%r9,%rax,8)
  movsd  (%rsi,%rax,8),%xmm0
  movsd  %xmm0,(%rcx,%rax,8)
  add    $0x1,%rax
  cmp    %rax,%rdx
  jne    L21
L55:
  mov    0x34(%rsp),%eax
  test   %eax,%eax
  jle    L40
  mov    0x34(%rsp),%eax
  movslq 0x30(%rsp),%r10
  mov    0x18(%rsp),%r9
  lea    0x1(%rax),%r8d
  lea    0x0(,%r10,8),%rsi
  mov    $0x1,%eax
  nopw   0x0(%rax,%rax,1)
L62:
  mov    (%rdi,%rax,8),%rcx
  mov    (%r9,%rax,8),%rdx
  add    $0x1,%rax
  movsd  (%rcx),%xmm0
  movsd  %xmm0,(%rdx)
  movsd  (%rcx,%rsi,1),%xmm0
  movsd  %xmm0,(%rdx,%rsi,1)
  cmp    %rax,%r8
  jne    L62
  cmpl   $0x1,0x34(%rsp)
  jle    L40
  movsd  -0x78(%rsp),%xmm7
  mov    $0x1,%r15d
  mov    %rdi,%rsi
  lea    0x0(,%r10,8),%rcx
  lea    0x8(%rcx),%rax
  lea    -0x8(%rcx),%r9
  movq   D41(%rip),%xmm14
  movsd  D0(%rip),%xmm12
  movapd %xmm7,%xmm4
  mov    %rax,0x20(%rsp)
  movslq 0x34(%rsp),%rax
  mulsd  %xmm7,%xmm4
  movsd  -0x10(%rsp),%xmm7
  movapd %xmm14,%xmm13
  mov    %rax,0x28(%rsp)
  movsd  %xmm4,-0x58(%rsp)
  movapd %xmm7,%xmm4
  mulsd  %xmm7,%xmm4
  movsd  %xmm4,-0x50(%rsp)
  movsd  D26(%rip),%xmm4
  movsd  %xmm4,-0x70(%rsp)
  nopl   0x0(%rax,%rax,1)
L54:
  mov    0x8(%rsp),%rax
  cmpl   $0x1,0x30(%rsp)
  mov    (%rsi,%r15,8),%rdi
  mov    0x8(%rsi,%r15,8),%r11
  mov    (%rax,%r15,8),%r8
  mov    0x8(%rax,%r15,8),%rbp
  mov    -0x8(%rax,%r15,8),%rbx
  mov    0x10(%rsp),%rax
  mov    (%rax,%r15,8),%r14
  jle    L46
  mov    0x18(%rsp),%rax
  mov    %rcx,%rdx
  mov    %rsi,%rcx
  mov    -0x8(%rsi,%r15,8),%r12
  mov    %r9,%rsi
  mov    %r15,%r9
  mov    (%rax,%r15,8),%r13
  mov    $0x1,%eax
  mov    %rcx,%r15
  nopw   0x0(%rax,%rax,1)
L64:
  movsd  (%r8,%rax,8),%xmm3
  movsd  (%r11,%rax,8),%xmm7
  movsd  0x8(%r8,%rax,8),%xmm0
  movsd  (%rdi,%rax,8),%xmm4
  movapd %xmm7,%xmm1
  movsd  0x0(%rbp,%rax,8),%xmm2
  movsd  %xmm7,-0x48(%rsp)
  movsd  0x8(%rdi,%rax,8),%xmm7
  addsd  %xmm3,%xmm0
  addsd  %xmm4,%xmm1
  movsd  (%rbx,%rax,8),%xmm8
  movapd %xmm3,%xmm6
  addsd  %xmm3,%xmm2
  movsd  %xmm7,-0x40(%rsp)
  movapd %xmm7,%xmm14
  movsd  -0x8(%rdi,%rax,8),%xmm7
  addsd  %xmm8,%xmm6
  movapd %xmm3,%xmm15
  addsd  %xmm4,%xmm14
  movsd  -0x8(%r8,%rax,8),%xmm5
  mulsd  %xmm12,%xmm0
  addsd  %xmm3,%xmm15
  movapd %xmm4,%xmm11
  movsd  (%r12,%rax,8),%xmm10
  mulsd  %xmm12,%xmm1
  addsd  %xmm7,%xmm11
  mulsd  %xmm12,%xmm2
  mulsd  %xmm12,%xmm6
  mulsd  %xmm12,%xmm14
  movsd  %xmm0,-0x20(%rsp)
  mulsd  %xmm12,%xmm11
  movapd %xmm0,%xmm9
  movsd  -0x8(%r11,%rax,8),%xmm0
  mulsd  %xmm1,%xmm9
  andpd  %xmm13,%xmm1
  addsd  %xmm7,%xmm0
  movsd  %xmm0,-0x38(%rsp)
  movapd %xmm8,%xmm0
  movq   %xmm9,%rcx
  movapd %xmm4,%xmm9
  subsd  %xmm15,%xmm0
  addsd  %xmm4,%xmm9
  addsd  0x0(%rbp,%rax,8),%xmm0
  divsd  -0x58(%rsp),%xmm0
  movsd  %xmm9,-0x30(%rsp)
  movsd  0x8(%rbx,%rax,8),%xmm9
  addsd  %xmm8,%xmm9
  subsd  %xmm3,%xmm8
  movsd  %xmm9,-0x28(%rsp)
  movapd %xmm5,%xmm9
  subsd  %xmm15,%xmm9
  addsd  0x8(%r8,%rax,8),%xmm9
  movapd %xmm2,%xmm15
  divsd  -0x50(%rsp),%xmm9
  addsd  %xmm9,%xmm0
  movapd %xmm3,%xmm9
  andpd  %xmm13,%xmm15
  divsd  -0x68(%rsp),%xmm0
  subsd  0x0(%rbp,%rax,8),%xmm9
  mulsd  %xmm2,%xmm2
  mulsd  %xmm9,%xmm15
  movapd %xmm6,%xmm9
  mulsd  %xmm6,%xmm6
  andpd  %xmm13,%xmm9
  mulsd  %xmm8,%xmm9
  movsd  -0x78(%rsp),%xmm8
  mulsd  %xmm12,%xmm15
  subsd  %xmm6,%xmm2
  movapd %xmm3,%xmm6
  mulsd  %xmm12,%xmm9
  subsd  %xmm5,%xmm6
  divsd  %xmm8,%xmm2
  mulsd  %xmm6,%xmm1
  movapd %xmm5,%xmm6
  addsd  %xmm3,%xmm5
  subsd  %xmm3,%xmm6
  subsd  %xmm9,%xmm15
  movsd  -0x18(%rsp),%xmm9
  mulsd  %xmm12,%xmm5
  mulsd  %xmm9,%xmm15
  mulsd  %xmm12,%xmm1
  divsd  %xmm8,%xmm15
  movsd  -0x38(%rsp),%xmm8
  addsd  %xmm15,%xmm2
  movapd %xmm9,%xmm15
  subsd  %xmm2,%xmm0
  movapd %xmm8,%xmm2
  andpd  %xmm13,%xmm2
  mulsd  %xmm6,%xmm2
  mulsd  -0x70(%rsp),%xmm2
  subsd  %xmm2,%xmm1
  movapd %xmm8,%xmm2
  mulsd  %xmm12,%xmm2
  mulsd  %xmm9,%xmm1
  movsd  -0x10(%rsp),%xmm9
  mulsd  %xmm2,%xmm5
  movq   %rcx,%xmm2
  divsd  %xmm9,%xmm1
  subsd  %xmm5,%xmm2
  divsd  %xmm9,%xmm2
  addsd  %xmm2,%xmm1
  subsd  %xmm1,%xmm0
  addsd  -0x8(%rsp),%xmm0
  mulsd  -0x60(%rsp),%xmm0
  movapd %xmm7,%xmm1
  subsd  %xmm4,%xmm7
  addsd  %xmm3,%xmm0
  movsd  %xmm0,(%r14,%rax,8)
  movsd  -0x30(%rsp),%xmm3
  movapd %xmm10,%xmm0
  movsd  -0x48(%rsp),%xmm5
  movsd  -0x40(%rsp),%xmm8
  movsd  -0x28(%rsp),%xmm6
  subsd  %xmm3,%xmm0
  subsd  %xmm3,%xmm1
  movapd %xmm4,%xmm3
  subsd  %xmm5,%xmm3
  movapd %xmm6,%xmm2
  mulsd  %xmm12,%xmm6
  andpd  %xmm13,%xmm2
  addsd  %xmm5,%xmm0
  addsd  %xmm8,%xmm1
  divsd  -0x58(%rsp),%xmm0
  divsd  -0x50(%rsp),%xmm1
  addsd  %xmm1,%xmm0
  movsd  -0x20(%rsp),%xmm1
  movsd  -0x78(%rsp),%xmm5
  divsd  -0x68(%rsp),%xmm0
  andpd  %xmm13,%xmm1
  mulsd  %xmm3,%xmm1
  movapd %xmm10,%xmm3
  addsd  %xmm4,%xmm10
  subsd  %xmm4,%xmm3
  mulsd  %xmm3,%xmm2
  movq   %rcx,%xmm3
  mulsd  -0x70(%rsp),%xmm2
  mulsd  %xmm12,%xmm1
  subsd  %xmm2,%xmm1
  movapd %xmm10,%xmm2
  mulsd  %xmm12,%xmm2
  mulsd  %xmm15,%xmm1
  mulsd  %xmm6,%xmm2
  divsd  %xmm5,%xmm1
  subsd  %xmm2,%xmm3
  divsd  %xmm5,%xmm3
  movapd %xmm4,%xmm5
  subsd  %xmm8,%xmm5
  movapd %xmm3,%xmm2
  movapd %xmm11,%xmm3
  addsd  %xmm1,%xmm2
  mulsd  %xmm11,%xmm3
  movapd %xmm14,%xmm1
  mulsd  %xmm14,%xmm14
  andpd  %xmm13,%xmm1
  mulsd  %xmm5,%xmm1
  movapd %xmm11,%xmm5
  andpd  %xmm13,%xmm5
  subsd  %xmm2,%xmm0
  movapd %xmm5,%xmm2
  mulsd  %xmm7,%xmm2
  mulsd  %xmm12,%xmm1
  mulsd  %xmm12,%xmm2
  subsd  %xmm2,%xmm1
  movapd %xmm14,%xmm2
  subsd  %xmm3,%xmm2
  mulsd  %xmm15,%xmm1
  divsd  %xmm9,%xmm2
  divsd  %xmm9,%xmm1
  addsd  %xmm2,%xmm1
  subsd  %xmm1,%xmm0
  addsd  (%rsp),%xmm0
  mulsd  -0x60(%rsp),%xmm0
  addsd  (%rdi,%rax,8),%xmm0
  movsd  %xmm0,0x0(%r13,%rax,8)
  add    $0x1,%rax
  cmp    %rax,%r10
  jne    L64
  mov    %r15,%rax
  mov    %rdx,%rcx
  mov    %r9,%r15
  mov    %rsi,%r9
  mov    %rax,%rsi
L46:
  movsd  (%rdi,%rcx,1),%xmm0
  addsd  (%r11,%rcx,1),%xmm0
  add    $0x1,%r15
  movsd  (%r8,%rcx,1),%xmm2
  movsd  0x0(%rbp,%rcx,1),%xmm5
  movsd  (%rbx,%rcx,1),%xmm4
  movsd  (%r8,%r9,1),%xmm7
  mulsd  %xmm12,%xmm0
  movapd %xmm2,%xmm3
  movapd %xmm2,%xmm8
  mov    0x20(%rsp),%rax
  addsd  %xmm5,%xmm3
  addsd  %xmm4,%xmm8
  movapd %xmm2,%xmm6
  movsd  (%rdi,%r9,1),%xmm11
  addsd  %xmm2,%xmm6
  movapd %xmm7,%xmm1
  movsd  (%r8,%rax,1),%xmm10
  addsd  (%r11,%r9,1),%xmm11
  mulsd  %xmm12,%xmm3
  mulsd  %xmm12,%xmm8
  movapd %xmm0,%xmm9
  movapd %xmm4,%xmm0
  subsd  %xmm6,%xmm0
  subsd  %xmm6,%xmm1
  movapd %xmm2,%xmm6
  subsd  %xmm5,%xmm6
  subsd  %xmm2,%xmm4
  addsd  %xmm5,%xmm0
  addsd  %xmm10,%xmm1
  divsd  -0x58(%rsp),%xmm0
  divsd  -0x50(%rsp),%xmm1
  movapd %xmm8,%xmm5
  addsd  %xmm1,%xmm0
  movapd %xmm3,%xmm1
  divsd  -0x68(%rsp),%xmm0
  mulsd  %xmm3,%xmm3
  andpd  %xmm13,%xmm1
  andpd  %xmm13,%xmm5
  mulsd  %xmm4,%xmm5
  movsd  -0x78(%rsp),%xmm4
  mulsd  %xmm6,%xmm1
  mulsd  %xmm8,%xmm8
  mulsd  %xmm12,%xmm5
  mulsd  %xmm12,%xmm1
  subsd  %xmm8,%xmm3
  divsd  %xmm4,%xmm3
  subsd  %xmm5,%xmm1
  movsd  -0x18(%rsp),%xmm5
  mulsd  %xmm5,%xmm1
  divsd  %xmm4,%xmm1
  movapd %xmm7,%xmm4
  subsd  %xmm2,%xmm4
  addsd  %xmm3,%xmm1
  movapd %xmm2,%xmm3
  subsd  %xmm7,%xmm3
  addsd  %xmm2,%xmm7
  subsd  %xmm1,%xmm0
  movapd %xmm9,%xmm1
  mulsd  %xmm12,%xmm7
  andpd  %xmm13,%xmm1
  mulsd  %xmm3,%xmm1
  movapd %xmm11,%xmm3
  andpd  %xmm13,%xmm3
  mulsd  %xmm4,%xmm3
  movapd %xmm11,%xmm4
  mulsd  -0x70(%rsp),%xmm3
  mulsd  %xmm12,%xmm4
  mulsd  %xmm12,%xmm1
  mulsd  %xmm7,%xmm4
  subsd  %xmm3,%xmm1
  movapd %xmm10,%xmm3
  addsd  %xmm2,%xmm3
  mulsd  %xmm5,%xmm1
  movsd  -0x10(%rsp),%xmm5
  mulsd  %xmm12,%xmm3
  divsd  %xmm5,%xmm1
  mulsd  %xmm9,%xmm3
  subsd  %xmm4,%xmm3
  divsd  %xmm5,%xmm3
  addsd  %xmm3,%xmm1
  subsd  %xmm1,%xmm0
  addsd  -0x8(%rsp),%xmm0
  mulsd  -0x60(%rsp),%xmm0
  addsd  %xmm2,%xmm0
  movsd  %xmm0,(%r14,%rcx,1)
  cmp    %r15,0x28(%rsp)
  jne    L54
  mov    %rsi,%rdi
L40:
  mov    0x30(%rsp),%ebx
  cmp    $0x1,%ebx
  jle    L43
  movsd  -0x78(%rsp),%xmm11
  movsd  -0x10(%rsp),%xmm15
  movslq %ebx,%r10
  movslq 0x34(%rsp),%rax
  mov    0x8(%rsp),%r9
  movapd %xmm11,%xmm7
  movapd %xmm15,%xmm13
  movsd  D26(%rip),%xmm4
  movsd  D0(%rip),%xmm12
  mulsd  %xmm11,%xmm7
  lea    0x0(,%rax,8),%r8
  mov    (%r9,%rax,8),%rcx
  mov    (%rdi,%rax,8),%rdx
  mulsd  %xmm15,%xmm13
  mov    0x8(%rdi,%r8,1),%rsi
  mov    -0x8(%rdi,%r8,1),%rdi
  movsd  %xmm4,-0x70(%rsp)
  movq   D41(%rip),%xmm14
  mov    -0x8(%r9,%r8,1),%r8
  mov    0x18(%rsp),%r9
  movsd  %xmm7,-0x78(%rsp)
  mov    (%r9,%rax,8),%r9
  mov    $0x1,%eax
  movsd  %xmm13,-0x58(%rsp)
  nopl   0x0(%rax,%rax,1)
L33:
  movsd  (%rdx,%rax,8),%xmm3
  movsd  -0x8(%rdx,%rax,8),%xmm8
  movsd  (%rcx,%rax,8),%xmm7
  movsd  (%r8,%rax,8),%xmm0
  movapd %xmm3,%xmm1
  addsd  0x8(%r8,%rax,8),%xmm0
  addsd  0x8(%rcx,%rax,8),%xmm7
  addsd  %xmm3,%xmm1
  movsd  (%rdi,%rax,8),%xmm5
  movapd %xmm8,%xmm9
  movsd  (%rsi,%rax,8),%xmm2
  movsd  0x8(%rdx,%rax,8),%xmm4
  movapd %xmm3,%xmm6
  mulsd  %xmm12,%xmm7
  movapd %xmm0,%xmm13
  movapd %xmm5,%xmm0
  subsd  %xmm1,%xmm9
  subsd  %xmm1,%xmm0
  movsd  0x8(%rdx,%rax,8),%xmm1
  movapd %xmm5,%xmm10
  subsd  %xmm3,%xmm10
  addsd  %xmm3,%xmm5
  addsd  %xmm3,%xmm4
  addsd  %xmm8,%xmm6
  addsd  %xmm9,%xmm1
  movapd %xmm3,%xmm9
  addsd  %xmm2,%xmm0
  divsd  -0x58(%rsp),%xmm1
  subsd  %xmm2,%xmm9
  divsd  -0x78(%rsp),%xmm0
  addsd  %xmm1,%xmm0
  movapd %xmm7,%xmm1
  andpd  %xmm14,%xmm1
  addsd  %xmm3,%xmm2
  divsd  -0x68(%rsp),%xmm0
  subsd  %xmm3,%xmm8
  mulsd  %xmm12,%xmm5
  mulsd  %xmm9,%xmm1
  mulsd  %xmm12,%xmm2
  mulsd  %xmm12,%xmm4
  mulsd  %xmm12,%xmm6
  mulsd  %xmm12,%xmm1
  mulsd  %xmm7,%xmm2
  movapd %xmm13,%xmm7
  mulsd  %xmm12,%xmm7
  movapd %xmm1,%xmm9
  movapd %xmm13,%xmm1
  andpd  %xmm14,%xmm1
  mulsd  %xmm10,%xmm1
  movsd  -0x18(%rsp),%xmm10
  mulsd  -0x70(%rsp),%xmm1
  mulsd  %xmm7,%xmm5
  subsd  %xmm1,%xmm9
  subsd  %xmm5,%xmm2
  movapd %xmm9,%xmm1
  mulsd  %xmm10,%xmm1
  divsd  %xmm11,%xmm2
  divsd  %xmm11,%xmm1
  addsd  %xmm2,%xmm1
  movapd %xmm3,%xmm2
  subsd  0x8(%rdx,%rax,8),%xmm2
  subsd  %xmm1,%xmm0
  movapd %xmm4,%xmm1
  mulsd  %xmm4,%xmm4
  andpd  %xmm14,%xmm1
  mulsd  %xmm2,%xmm1
  movapd %xmm6,%xmm2
  mulsd  %xmm6,%xmm6
  andpd  %xmm14,%xmm2
  mulsd  %xmm8,%xmm2
  mulsd  %xmm12,%xmm1
  subsd  %xmm6,%xmm4
  mulsd  %xmm12,%xmm2
  divsd  %xmm15,%xmm4
  subsd  %xmm2,%xmm1
  mulsd  %xmm10,%xmm1
  divsd  %xmm15,%xmm1
  addsd  %xmm4,%xmm1
  subsd  %xmm1,%xmm0
  addsd  (%rsp),%xmm0
  mulsd  -0x60(%rsp),%xmm0
  addsd  %xmm3,%xmm0
  movsd  %xmm0,(%r9,%rax,8)
  add    $0x1,%rax
  cmp    %r10,%rax
  jne    L33
L43:
  add    $0x38,%rsp
  pop    %rbx
  pop    %rbp
  pop    %r12
  pop    %r13
  pop    %r14
  pop    %r15
  ret
```

tool_calls: name: parse_data
arguments: data_tag: D41
type_infered: qword
name: parse_data
arguments: data_tag: D0
type_infered: byte[8]
name: parse_data
arguments: data_tag: D26
type_infered: byte[8]

tool: D41: 9223372036854775807

tool: {"D0": [0x00,0x00,0x00,0x00,0x00,0x00,0xe0,0x3f]}

tool: {"D26": [0x00,0x00,0x00,0x00,0x00,0x00,0xd0,0x3f]}

assistant: ```c
void calculate_fg(double Re, double GX, double GY, double alpha, double dt, double dx, double dy, int imax, int jmax, double **U, double **V, double **F, double **G) {
  int i;
  int j;
  double u_frd_sum_i;
  double u_bkd_sum_i;
  double v_frd_sum_i;
  double v_bkd_sum_i;
  double u_frd_sum_j;
  double u_bkd_sum_j;
  double v_frd_sum_j;
  double v_bkd_sum_j;
  double d2ux;
  double d2uy;
  double du2x;
  double duvy;
  double d2vx;
  double d2vy;
  double duvx;
  double dv2y;
  for (j = 1; j < jmax + 1; j++) {
    F[0][j] = U[0][j];
    F[imax][j] = U[imax][j];
  }
  for (i = 1; i < imax + 1; i++) {
    G[i][0] = V[i][0];
    G[i][jmax] = V[i][jmax];
  }
  for (i = 1; i < imax; i++) {
    for (j = 1; j < jmax; j++) {
      u_frd_sum_i = (U[i][j] + U[i + 1][j]) / 2;
      u_frd_sum_j = (U[i][j] + U[i][j + 1]) / 2;
      u_bkd_sum_i = (U[i][j] + U[i - 1][j]) / 2;
      u_bkd_sum_j = (U[i][j] + U[i][j - 1]) / 2;
      v_frd_sum_i = (V[i][j] + V[i + 1][j]) / 2;
      v_frd_sum_j = (V[i][j] + V[i][j + 1]) / 2;
      v_bkd_sum_i = (V[i][j] + V[i - 1][j]) / 2;
      v_bkd_sum_j = (V[i][j] + V[i][j - 1]) / 2;
      d2ux = (U[i - 1][j] - 2 * U[i][j] + U[i + 1][j]) / (dx * dx);
      d2uy = (U[i][j - 1] - 2 * U[i][j] + U[i][j + 1]) / (dy * dy);
      du2x = (u_frd_sum_i * u_frd_sum_i - u_bkd_sum_i * u_bkd_sum_i) / dx + alpha * (fabs(u_frd_sum_i) * (U[i][j] - U[i + 1][j]) / 2 - fabs(u_bkd_sum_i) * (U[i - 1][j] - U[i][j]) / 2) / dx;
      duvy = (v_frd_sum_i * u_frd_sum_j - (V[i][j - 1] + V[i + 1][j - 1]) / 2 * u_bkd_sum_j) / dy + alpha * (fabs(v_frd_sum_i) * (U[i][j] - U[i][j - 1]) / 2 - fabs(V[i][j - 1] + V[i + 1][j - 1]) * (U[i][j - 1] - U[i][j]) / 4) / dy;
      d2vx = (V[i - 1][j] - 2 * V[i][j] + V[i + 1][j]) / (dx * dx);
      d2vy = (V[i][j - 1] - 2 * V[i][j] + V[i][j + 1]) / (dy * dy);
      dv2y = (v_frd_sum_j * v_frd_sum_j - v_bkd_sum_j * v_bkd_sum_j) / dy + alpha * (fabs(v_frd_sum_j) * (V[i][j] - V[i][j + 1]) / 2 - fabs(v_bkd_sum_j) * (V[i][j - 1] - V[i][j]) / 2) / dy;
      duvx = (u_frd_sum_j * v_frd_sum_i - (U[i - 1][j] + U[i - 1][j + 1]) / 2 * v_bkd_sum_i) / dx + alpha * (fabs(u_frd_sum_j) * (V[i][j] - V[i + 1][j]) / 2 - fabs(U[i - 1][j] + U[i - 1][j + 1]) * (V[i - 1][j] - V[i][j]) / 4) / dx;
      F[i][j] = U[i][j] + dt * ((d2ux + d2uy) / Re - du2x - duvy + GX);
      G[i][j] = V[i][j] + dt * ((d2vx + d2vy) / Re - duvx - dv2y + GY);
    }
    j = jmax;
    u_frd_sum_i = (U[i][j] + U[i + 1][j]) / 2;
    u_frd_sum_j = (U[i][j] + U[i][j + 1]) / 2;
    u_bkd_sum_i = (U[i][j] + U[i - 1][j]) / 2;
    u_bkd_sum_j = (U[i][j] + U[i][j - 1]) / 2;
    v_frd_sum_i = (V[i][j] + V[i + 1][j]) / 2;
    d2ux = (U[i - 1][j] - 2 * U[i][j] + U[i + 1][j]) / (dx * dx);
    d2uy = (U[i][j - 1] - 2 * U[i][j] + U[i][j + 1]) / (dy * dy);
    du2x = (u_frd_sum_i * u_frd_sum_i - u_bkd_sum_i * u_bkd_sum_i) / dx + alpha * (fabs(u_frd_sum_i) * (U[i][j] - U[i + 1][j]) / 2 - fabs(u_bkd_sum_i) * (U[i - 1][j] - U[i][j]) / 2) / dx;
    duvy = (v_frd_sum_i * u_frd_sum_j - (V[i][j - 1] + V[i + 1][j - 1]) / 2 * u_bkd_sum_j) / dy + alpha * (fabs(v_frd_sum_i) * (U[i][j] - U[i][j - 1]) / 2 - fabs(V[i][j - 1] + V[i + 1][j - 1]) * (U[i][j - 1] - U[i][j]) / 4) / dy;
    F[i][j] = U[i][j] + dt * ((d2ux + d2uy) / Re - du2x - duvy + GX);
  }
  i = imax;
  for (j = 1; j < jmax; j++) {
    u_frd_sum_j = (U[i][j] + U[i][j + 1]) / 2;
    v_frd_sum_i = (V[i][j] + V[i + 1][j]) / 2;
    v_frd_sum_j = (V[i][j] + V[i][j + 1]) / 2;
    v_bkd_sum_i = (V[i][j] + V[i - 1][j]) / 2;
    v_bkd_sum_j = (V[i][j] + V[i][j - 1]) / 2;
    d2vx = (V[i - 1][j] - 2 * V[i][j] + V[i + 1][j]) / (dx * dx);
    d2vy = (V[i][j - 1] - 2 * V[i][j] + V[i][j + 1]) / (dy * dy);
    dv2y = (v_frd_sum_j * v_frd_sum_j - v_bkd_sum_j * v_bkd_sum_j) / dy + alpha * (fabs(v_frd_sum_j) * (V[i][j] - V[i][j + 1]) / 2 - fabs(v_bkd_sum_j) * (V[i][j - 1] - V[i][j]) / 2) / dy;
    duvx = (u_frd_sum_j * v_frd_sum_i - (U[i - 1][j] + U[i - 1][j + 1]) / 2 * v_bkd_sum_i) / dx + alpha * (fabs(u_frd_sum_j) * (V[i][j] - V[i + 1][j]) / 2 - fabs(U[i - 1][j] + U[i - 1][j + 1]) * (V[i - 1][j] - V[i][j]) / 4) / dx;
    G[i][j] = V[i][j] + dt * ((d2vx + d2vy) / Re - duvx - dv2y + GY);
  }
}
```